{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-05-06T00:09:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-05-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":2736,"title":"Pernicious Anniversary Problem","description":"Since Cody is 5 years old, it's pernicious. A \u003chttp://rosettacode.org/wiki/Pernicious_numbers Pernicious number\u003e is an integer whose population count is a prime. Check if the given number is pernicious.","description_html":"\u003cp\u003eSince Cody is 5 years old, it's pernicious. A \u003ca href = \"http://rosettacode.org/wiki/Pernicious_numbers\"\u003ePernicious number\u003c/a\u003e is an integer whose population count is a prime. Check if the given number is pernicious.\u003c/p\u003e","function_template":"function y = isPernicious(x)\r\n  y = false;\r\nend","test_suite":"%%\r\nx = 5;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 1;\r\ny_correct = false;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 2^randi(16);\r\ny_correct = false;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 17;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 18;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 61;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 6;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 2115;\r\ny_correct = false;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 2114;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 2017;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":13,"comments_count":1,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":840,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":34,"created_at":"2014-12-08T08:48:45.000Z","updated_at":"2026-05-03T23:00:10.000Z","published_at":"2017-10-16T01:45:06.000Z","restored_at":"2017-10-25T14:37:50.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince Cody is 5 years old, it's pernicious. A\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://rosettacode.org/wiki/Pernicious_numbers\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePernicious number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer whose population count is a prime. Check if the given number is pernicious.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":248,"title":"Twins in a Window","description":"\u003chttp://en.wikipedia.org/wiki/Twin_primes Twin primes\u003e are prime numbers that differ by 2, such as [11,13] or [41,43]. Write a function that returns a sorted list of the twin primes between lowVal and highVal (all the primes must be greater than lowVal and less than highVal). The primes should be arranged in an n-by-2 matrix as shown in the examples below.\r\n\r\nExamples:\r\n\r\n Input  lowVal = 10, highVal = 50\r\n Output p is [ 11    13\r\n               17    19\r\n               29    31\r\n               41    43 ]\r\n\r\n Input  lowVal = 1000, highVal = 1050\r\n Output p is [ 1019  1021\r\n               1031  1033 ]\r\n","description_html":"\u003cp\u003e\u003ca href=\"http://en.wikipedia.org/wiki/Twin_primes\"\u003eTwin primes\u003c/a\u003e are prime numbers that differ by 2, such as [11,13] or [41,43]. Write a function that returns a sorted list of the twin primes between lowVal and highVal (all the primes must be greater than lowVal and less than highVal). The primes should be arranged in an n-by-2 matrix as shown in the examples below.\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cpre\u003e Input  lowVal = 10, highVal = 50\r\n Output p is [ 11    13\r\n               17    19\r\n               29    31\r\n               41    43 ]\u003c/pre\u003e\u003cpre\u003e Input  lowVal = 1000, highVal = 1050\r\n Output p is [ 1019  1021\r\n               1031  1033 ]\u003c/pre\u003e","function_template":"function p = window_twins(lowVal,highVal)\r\n  p = 0;\r\nend","test_suite":"%%\r\nlowVal = 10;\r\nhighVal = 50;\r\np = [11    13\r\n     17    19\r\n     29    31\r\n     41    43];\r\nassert(isequal(window_twins(lowVal,highVal),p))\r\n\r\n%%\r\nlowVal = 1000;\r\nhighVal = 1050;\r\np = [1019  1021\r\n     1031  1033];\r\nassert(isequal(window_twins(lowVal,highVal),p))\r\n\r\n%%\r\nlowVal = 3120;\r\nhighVal = 3300;\r\np = [ 3167  3169\r\n      3251  3253\r\n      3257  3259];\r\nassert(isequal(window_twins(lowVal,highVal),p))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":7,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":162,"test_suite_updated_at":"2012-02-03T17:12:57.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-03T16:30:52.000Z","updated_at":"2026-04-10T14:29:19.000Z","published_at":"2012-02-03T17:12:56.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Twin_primes\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eTwin primes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e are prime numbers that differ by 2, such as [11,13] or [41,43]. Write a function that returns a sorted list of the twin primes between lowVal and highVal (all the primes must be greater than lowVal and less than highVal). The primes should be arranged in an n-by-2 matrix as shown in the examples below.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input  lowVal = 10, highVal = 50\\n Output p is [ 11    13\\n               17    19\\n               29    31\\n               41    43 ]\\n\\n Input  lowVal = 1000, highVal = 1050\\n Output p is [ 1019  1021\\n               1031  1033 ]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44230,"title":"I'm going to enjoy watching you calculate, Mr Anderson","description":"Smith numbers are numbers such that if you add up all of the digits in the number, that sum equals the sum of all of the digits in all of their factors. This term was coined by Albert Wilansky, when he noticed the defining property in the phone number of his brother-in-law Harold Smith: 493-7775.\r\n4+9+3+7+7+7+5=42\r\nThe prime factors of 4937775 are 3, 5, 5, and 65837. 3+5+5+(6+5+8+3+7) = 42\r\nSince all prime numbers obviously meet this criteria, Smith numbers are defined as composite numbers. Write a MATLAB function that will tell you if a given number is a Smith number.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 174px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 87px; transform-origin: 407px 87px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.5px 8px; transform-origin: 375.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSmith numbers are numbers such that if you add up all of the digits in the number, that sum equals the sum of all of the digits in all of their factors. This term was coined by Albert Wilansky, when he noticed the defining property in the phone number of his brother-in-law Harold Smith: 493-7775.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64px 8px; transform-origin: 64px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4+9+3+7+7+7+5=42\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251px 8px; transform-origin: 251px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe prime factors of 4937775 are 3, 5, 5, and 65837. 3+5+5+(6+5+8+3+7) = 42\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.5px 8px; transform-origin: 380.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSince all prime numbers obviously meet this criteria, Smith numbers are defined as composite numbers. Write a MATLAB function that will tell you if a given number is a Smith number.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = smith(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nassert(isequal(smith(4937775),1))\r\n%%\r\nassert(isequal(smith(1164),0))\r\n%%\r\nassert(isequal(smith(19683),1))\r\n%%\r\nassert(isequal(smith(11),0))  % Remember - Smith numbers are composite\r\n%%\r\nassert(isequal(smith(11^2),1))\r\n%%\r\nassert(isequal(smith(345741),1))\r\n%%\r\nassert(isequal(smith(19876),0))\r\n%%\r\nassert(isequal(smith(314159),0))\r\n%%\r\nassert(isequal(smith(612985),1))\r\n%%\r\nassert(isequal(smith(12379887),1))\r\n%%\r\nassert(isequal(smith(23456789),0))\r\n%%\r\nassert(isequal(smith(13),0))\r\n%%\r\nassert(isequal(smith(23),0))\r\n%%\r\ny=primes(randi(1e5));\r\nassert(isequal(smith(y(end)),0))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":1615,"edited_by":223089,"edited_at":"2023-01-07T08:26:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":49,"test_suite_updated_at":"2023-01-07T08:26:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-06-01T19:16:25.000Z","updated_at":"2026-03-16T15:29:16.000Z","published_at":"2017-06-01T19:16:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSmith numbers are numbers such that if you add up all of the digits in the number, that sum equals the sum of all of the digits in all of their factors. This term was coined by Albert Wilansky, when he noticed the defining property in the phone number of his brother-in-law Harold Smith: 493-7775.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e4+9+3+7+7+7+5=42\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe prime factors of 4937775 are 3, 5, 5, and 65837. 3+5+5+(6+5+8+3+7) = 42\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince all prime numbers obviously meet this criteria, Smith numbers are defined as composite numbers. Write a MATLAB function that will tell you if a given number is a Smith number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44384,"title":"Find the nearest prime number","description":"Happy 5th birthday, Cody! Since 5 is a prime number, let's have some fun looking for other prime numbers.\r\n\r\nGiven a positive integer x, find the nearest prime number. Keep in mind that the nearest prime may be less than x.\r\n\r\n*Examples*\r\n\r\n  nearestprime(5) = 5\r\n  nearestprime(36) = 37\r\n  nearestprime(200) = 199\r\n\r\nNOTE: You may ignore cases in which two prime numbers are equally close to x. (e.g., x=12 --\u003e 11 and 13 are both primes). ","description_html":"\u003cp\u003eHappy 5th birthday, Cody! Since 5 is a prime number, let's have some fun looking for other prime numbers.\u003c/p\u003e\u003cp\u003eGiven a positive integer x, find the nearest prime number. Keep in mind that the nearest prime may be less than x.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003enearestprime(5) = 5\r\nnearestprime(36) = 37\r\nnearestprime(200) = 199\r\n\u003c/pre\u003e\u003cp\u003eNOTE: You may ignore cases in which two prime numbers are equally close to x. (e.g., x=12 --\u0026gt; 11 and 13 are both primes).\u003c/p\u003e","function_template":"function y = nearestprime(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 0;\r\ny_correct = 2;\r\nassert(isequal(nearestprime(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 5;\r\nassert(isequal(nearestprime(x),y_correct))\r\n\r\n%%\r\nx = 100;\r\ny_correct = 101;\r\nassert(isequal(nearestprime(x),y_correct))\r\n\r\n%%\r\nx = 500;\r\ny_correct = 499;\r\nassert(isequal(nearestprime(x),y_correct))\r\n\r\n%%\r\nx = 911;\r\ny_correct = 911;\r\nassert(isequal(nearestprime(x),y_correct))\r\n\r\n%%\r\nx = 2500;\r\ny_correct = 2503;\r\nassert(isequal(nearestprime(x),y_correct))\r\n\r\n%%\r\nx = 8000;\r\ny_correct = 7993;\r\nassert(isequal(nearestprime(x),y_correct))\r\n\r\n%%\r\nx = 100000;\r\ny_correct = 100003;\r\nassert(isequal(nearestprime(x),y_correct))\r\n\r\n%%\r\nx = 1300000;\r\ny_correct = 1299989;\r\nassert(isequal(nearestprime(x),y_correct))\r\n\r\n%%\r\nx = 179424710;\r\ny_correct = 179424719;\r\nassert(isequal(nearestprime(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":9,"comments_count":1,"created_by":4793,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":664,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":34,"created_at":"2017-10-13T19:42:15.000Z","updated_at":"2026-04-07T15:16:58.000Z","published_at":"2017-10-16T01:45:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHappy 5th birthday, Cody! Since 5 is a prime number, let's have some fun looking for other prime numbers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a positive integer x, find the nearest prime number. Keep in mind that the nearest prime may be less than x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[nearestprime(5) = 5\\nnearestprime(36) = 37\\nnearestprime(200) = 199]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNOTE: You may ignore cases in which two prime numbers are equally close to x. (e.g., x=12 --\u0026gt; 11 and 13 are both primes).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":3016,"title":"Twin Primes","description":"Twin primes are pairs of primes that are immediately next to each other (difference of two). The lesser of twin primes are 3, 5, 11, 17, 29, ... ( \u003chttp://oeis.org/A001359 ref.\u003e ). The greater of twin primes are 5, 7, 13, 19, 31, ... ( \u003chttp://oeis.org/A006512 ref.\u003e ). Therefore, the first five twin primes are [3,5] [5,7] [11,13] [17,19] [29,31].\r\n\r\nFor a given index range n, return the twin primes corresponding to that range as a two-row column array.","description_html":"\u003cp\u003eTwin primes are pairs of primes that are immediately next to each other (difference of two). The lesser of twin primes are 3, 5, 11, 17, 29, ... ( \u003ca href = \"http://oeis.org/A001359\"\u003eref.\u003c/a\u003e ). The greater of twin primes are 5, 7, 13, 19, 31, ... ( \u003ca href = \"http://oeis.org/A006512\"\u003eref.\u003c/a\u003e ). Therefore, the first five twin primes are [3,5] [5,7] [11,13] [17,19] [29,31].\u003c/p\u003e\u003cp\u003eFor a given index range n, return the twin primes corresponding to that range as a two-row column array.\u003c/p\u003e","function_template":"function [twins] = twin_primes(n)\r\n\r\ntwins = n;\r\n\r\nend","test_suite":"%%\r\nn = 1:5;\r\ntwins_corr = [3, 5, 11, 17, 29; 5, 7, 13, 19, 31];\r\nassert(isequal(twin_primes(n),twins_corr))\r\n\r\n%%\r\nn = 1:10;\r\ntwins_corr = [3, 5, 11, 17, 29, 41, 59, 71, 101, 107; 5, 7, 13, 19, 31, 43, 61, 73, 103, 109];\r\nassert(isequal(twin_primes(n),twins_corr))\r\n\r\n%%\r\nn = 1:25;\r\ntwins_corr = [3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521; 5, 7, 13, 19, 31, 43, 61, 73, 103, 109, 139, 151, 181, 193, 199, 229, 241, 271, 283, 313, 349, 421, 433, 463, 523];\r\nassert(isequal(twin_primes(n),twins_corr))\r\n\r\n%%\r\nn = 1:51;\r\ntwins_corr = [3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481, 1487, 1607; 5, 7, 13, 19, 31, 43, 61, 73, 103, 109, 139, 151, 181, 193, 199, 229, 241, 271, 283, 313, 349, 421, 433, 463, 523, 571, 601, 619, 643, 661, 811, 823, 829, 859, 883, 1021, 1033, 1051, 1063, 1093, 1153, 1231, 1279, 1291, 1303, 1321, 1429, 1453, 1483, 1489, 1609];\r\nassert(isequal(twin_primes(n),twins_corr))\r\n\r\n%%\r\nn = 10:29;\r\ntwins_corr = [107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641; 109, 139, 151, 181, 193, 199, 229, 241, 271, 283, 313, 349, 421, 433, 463, 523, 571, 601, 619, 643];\r\nassert(isequal(twin_primes(n),twins_corr))\r\n\r\n%%\r\nn = 2:8;\r\ntwins_corr = [5, 11, 17, 29, 41, 59, 71; 7, 13, 19, 31, 43, 61, 73];\r\nassert(isequal(twin_primes(n),twins_corr))\r\n\r\n%%\r\nn = 35:42;\r\ntwins_corr = [881, 1019, 1031, 1049, 1061, 1091, 1151, 1229; 883, 1021, 1033, 1051, 1063, 1093, 1153, 1231];\r\nassert(isequal(twin_primes(n),twins_corr))\r\n\r\n%%\r\nn = 34:47;\r\ntwins_corr = [857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427; 859, 883, 1021, 1033, 1051, 1063, 1093, 1153, 1231, 1279, 1291, 1303, 1321, 1429];\r\nassert(isequal(twin_primes(n),twins_corr))\r\n\r\n%%\r\nn = 9:-1:4;\r\ntwins_corr = [101, 71, 59, 41, 29, 17; 103, 73, 61, 43, 31, 19];\r\nassert(isequal(twin_primes(n),twins_corr))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":98,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":30,"created_at":"2015-02-14T03:03:50.000Z","updated_at":"2026-03-16T14:18:09.000Z","published_at":"2015-02-14T03:03:50.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTwin primes are pairs of primes that are immediately next to each other (difference of two). The lesser of twin primes are 3, 5, 11, 17, 29, ... (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://oeis.org/A001359\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eref.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e ). The greater of twin primes are 5, 7, 13, 19, 31, ... (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://oeis.org/A006512\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eref.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e ). Therefore, the first five twin primes are [3,5] [5,7] [11,13] [17,19] [29,31].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given index range n, return the twin primes corresponding to that range as a two-row column array.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44385,"title":"Extra safe primes","description":"Did you know that the number 5 is the first safe prime? A safe prime is a prime number that can be expressed as 2p+1, where p is also a prime.\r\n\r\nTo celebrate Cody's Five-Year Anniversary, write a function to determine if a positive integer n is a safe prime in which the prime p (such that n=2p+1) is *also a safe prime*.\r\n\r\n*Examples*\r\n\r\n  isextrasafe(5) = false % because 5=2*2+1 and 2 is not a safe prime\r\n  isextrasafe(23) = true % because 23=2*11+1 and 11 is also a safe prime (11=2*5+1)\r\n","description_html":"\u003cp\u003eDid you know that the number 5 is the first safe prime? A safe prime is a prime number that can be expressed as 2p+1, where p is also a prime.\u003c/p\u003e\u003cp\u003eTo celebrate Cody's Five-Year Anniversary, write a function to determine if a positive integer n is a safe prime in which the prime p (such that n=2p+1) is \u003cb\u003ealso a safe prime\u003c/b\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eisextrasafe(5) = false % because 5=2*2+1 and 2 is not a safe prime\r\nisextrasafe(23) = true % because 23=2*11+1 and 11 is also a safe prime (11=2*5+1)\r\n\u003c/pre\u003e","function_template":"function tf = isextrasafe(x)\r\n    tf = false;\r\nend","test_suite":"%%\r\nx = 0;\r\nassert(isequal(isextrasafe(x),false))\r\n\r\n%%\r\nx = 5;\r\nassert(isequal(isextrasafe(x),false))\r\n\r\n%%\r\nx = 7;\r\nassert(isequal(isextrasafe(x),false))\r\n\r\n%%\r\nx = 11;\r\nassert(isequal(isextrasafe(x),true))\r\n\r\n%%\r\nx = 15;\r\nassert(isequal(isextrasafe(x),false))\r\n\r\n%%\r\nx = 23;\r\nassert(isequal(isextrasafe(x),true))\r\n\r\n%%\r\nx = 71;\r\nassert(isequal(isextrasafe(x),false))\r\n\r\n%%\r\nx = 719;\r\nassert(isequal(isextrasafe(x),true))\r\n\r\n%%\r\nx = 2039;\r\nassert(isequal(isextrasafe(x),true))\r\n\r\n%%\r\nx = 2040;\r\nassert(isequal(isextrasafe(x),false))\r\n\r\n%%\r\nx = 5807;\r\nassert(isequal(isextrasafe(x),true))","published":true,"deleted":false,"likes_count":13,"comments_count":4,"created_by":4793,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":759,"test_suite_updated_at":"2017-10-19T17:09:19.000Z","rescore_all_solutions":true,"group_id":34,"created_at":"2017-10-13T20:02:13.000Z","updated_at":"2026-05-05T05:38:20.000Z","published_at":"2017-10-16T01:45:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDid you know that the number 5 is the first safe prime? A safe prime is a prime number that can be expressed as 2p+1, where p is also a prime.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo celebrate Cody's Five-Year Anniversary, write a function to determine if a positive integer n is a safe prime in which the prime p (such that n=2p+1) is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ealso a safe prime\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[isextrasafe(5) = false % because 5=2*2+1 and 2 is not a safe prime\\nisextrasafe(23) = true % because 23=2*11+1 and 11 is also a safe prime (11=2*5+1)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1204,"title":"Prime Time","description":"All you need to do here is submit your solution a prime number of seconds after the top of the hour.  Any hour at all...  Easy, right?","description_html":"\u003cp\u003eAll you need to do here is submit your solution a prime number of seconds after the top of the hour.  Any hour at all...  Easy, right?\u003c/p\u003e","function_template":"function y = prime_time(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('prime_time.m')\r\nassert(isempty(strfind(filetext, 'fopen')))\r\n%%\r\nx=123\r\ny = prime_time(x)\r\na=clock\r\nb=floor(polyval(a(5:6),60))\r\nif isprime(b)\r\ny_correct= y\r\nelse \r\ny_correct = NaN; \r\nend\r\nassert(isequal(y,y_correct),sprintf('%s%g%s','Time is ',datestr(now,13),', or ',b,' seconds after the hour.'))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":63,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-01-14T18:34:19.000Z","updated_at":"2025-11-22T17:34:33.000Z","published_at":"2013-01-14T18:34:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAll you need to do here is submit your solution a prime number of seconds after the top of the hour. Any hour at all... Easy, right?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":896,"title":"Sophie Germain prime","description":"In number theory, a prime number p is a *Sophie Germain prime* if 2p + 1 is also prime. For example, 23 is a Sophie Germain prime because it is a prime and 2 × 23 + 1 = 47, and 47 is also a prime number. These numbers are named after French mathematician Marie-Sophie Germain.\r\n\r\nSee \u003chttp://en.wikipedia.org/wiki/Sophie_Germain_prime Sophie Germain prime\u003e article on Wikipedia.\r\n\r\n\r\nIn this Problem , the input is a number and you must return true or false if this number is a Sophie Germain prime.","description_html":"\u003cp\u003eIn number theory, a prime number p is a \u003cb\u003eSophie Germain prime\u003c/b\u003e if 2p + 1 is also prime. For example, 23 is a Sophie Germain prime because it is a prime and 2 × 23 + 1 = 47, and 47 is also a prime number. These numbers are named after French mathematician Marie-Sophie Germain.\u003c/p\u003e\u003cp\u003eSee \u003ca href=\"http://en.wikipedia.org/wiki/Sophie_Germain_prime\"\u003eSophie Germain prime\u003c/a\u003e article on Wikipedia.\u003c/p\u003e\u003cp\u003eIn this Problem , the input is a number and you must return true or false if this number is a Sophie Germain prime.\u003c/p\u003e","function_template":"function tf = your_fcn_name(x)\r\n  tf = true;\r\nend","test_suite":"%%\r\np = 233;\r\ny_correct = true;\r\nassert(isequal(your_fcn_name(p),y_correct))\r\n\r\n%%\r\np = 23;\r\ny_correct14 = true;\r\nassert(isequal(your_fcn_name(p),y_correct14))\r\n\r\n%%\r\np = 22;\r\ny_correct14 = false;\r\nassert(isequal(your_fcn_name(p),y_correct14))\r\n\r\n%% \r\np = 1 % p must also be a prime number !!\r\ny_correct1t = false;\r\nassert(isequal(your_fcn_name(p),y_correct1t))\r\n\r\n%% \r\np = 14 % p must also be a prime number !!\r\ncorrect1t = false;\r\nassert(isequal(your_fcn_name(p),correct1t))\r\n\r\n%% \r\np = 29 \r\ncorrect1tp = true;\r\nassert(isequal(your_fcn_name(p),correct1tp))\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":2,"created_by":639,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1069,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":44,"created_at":"2012-08-10T13:04:11.000Z","updated_at":"2026-05-08T12:50:50.000Z","published_at":"2012-08-10T13:04:11.000Z","restored_at":"2018-10-10T14:57:27.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn number theory, a prime number p is a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSophie Germain prime\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if 2p + 1 is also prime. For example, 23 is a Sophie Germain prime because it is a prime and 2 × 23 + 1 = 47, and 47 is also a prime number. These numbers are named after French mathematician Marie-Sophie Germain.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Sophie_Germain_prime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSophie Germain prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e article on Wikipedia.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this Problem , the input is a number and you must return true or false if this number is a Sophie Germain prime.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2337,"title":"Sum of big primes without primes","description":"Inspired by Project Euler n°10 (I am quite obviously a fan).\r\nWith problem n°250 by Doug, you can find some global methods to compute the sum of all the primes below the input n.\r\nFor example, the sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.\r\nBut how to proceed (in time) with big number and WITHOUT the primes function ?\r\nHINTS: sum(primes(n)) is possible here but why miss the wonderfull Sieve of Eratosthenes ?\r\nhttp://en.wikipedia.org/wiki/Sieve_of_Eratosthenes","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 171px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 85.5px; transform-origin: 407px 85.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 183px 8px; transform-origin: 183px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInspired by Project Euler n°10 (I am quite obviously a fan).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376px 8px; transform-origin: 376px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWith problem n°250 by Doug, you can find some global methods to compute the sum of all the primes below the input n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 208px 8px; transform-origin: 208px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 255.5px 8px; transform-origin: 255.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBut how to proceed (in time) with big number and WITHOUT the primes function ?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 288.5px 8px; transform-origin: 288.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHINTS: sum(primes(n)) is possible here but why miss the wonderfull Sieve of Eratosthenes ?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttp://en.wikipedia.org/wiki/Sieve_of_Eratosthenes\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = big_euler10(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('big_euler10.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'primes'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 10;\r\ny_correct = 17;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 100;\r\ny_correct = 1060;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 1000;\r\ny_correct = 76127;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 10000;\r\ny_correct = 5736396;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 100000;\r\ny_correct = 454396537;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 1000000;\r\ny_correct = 37550402023;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 1000000-100;\r\ny_correct = 37542402433;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 2000000-1000;\r\ny_correct = 142781862782;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%% Solution of Project Euler 10 with n=2000000\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":3,"created_by":5390,"edited_by":223089,"edited_at":"2023-06-05T10:25:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":241,"test_suite_updated_at":"2023-06-05T10:25:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-05-27T21:25:58.000Z","updated_at":"2026-04-26T18:32:38.000Z","published_at":"2014-05-27T21:51:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInspired by Project Euler n°10 (I am quite obviously a fan).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWith problem n°250 by Doug, you can find some global methods to compute the sum of all the primes below the input n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBut how to proceed (in time) with big number and WITHOUT the primes function ?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHINTS: sum(primes(n)) is possible here but why miss the wonderfull Sieve of Eratosthenes ?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://en.wikipedia.org/wiki/Sieve_of_Eratosthenes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44403,"title":"Goldbach's marginal conjecture - Write integer as sum of three primes","description":"Goldbach's strong conjecture states that every even integer greater than 2 can be expressed as the sum of two primes. For example: 4 = 2+2, 6 = 3+3, 8 = 3+5, 10 = 3+7 = 5+5, 12 = 5+7 etc.\r\n\r\nAs a corrollary, Goldbach's weak conjecture states that every odd integer greater than 7 can be expressed as the sum of three odd primes. For example: 9 = 3+3+3, 11 = 3+3+5, 13 = 3+3+7 = 3+5+5, 15 = 3+5+7 = 5+5+5 etc.\r\n\r\nA third conjecture was written by Goldbach in the margin of a letter, and (in its modern version) states that \r\n\r\n\" _Every integer greater than 5 can be expressed as the sum of three primes._ \"\r\n\r\nExamples:\r\n\r\n*  6 = 2 + 2 + 2\r\n*  7 = 2 + 2 + 3\r\n*  8 = 2 + 3 + 3 \r\n*  9 = 2 + 2 + 5 = 3 + 3 + 3 \r\n* 10 = 2 + 3 + 5\r\n* 11 = 2 + 2 + 7 = 3 + 3 + 5\r\n* 12 = 2 + 3 + 7 = 2 + 5 + 5\r\n* 13 = 3 + 3 + 7 = 3 + 5 + 5\r\n* 14 = 2 + 5 + 7\r\n* 15 = 2 + 2 + 11 = 3 + 5 + 7 = 5 + 5 + 5\r\n\r\nYour task is to write a function which takes a positive integer _n_ as input, and which returns a 1-by-3 vector _y_, which contains three numbers that are primes and whose sum equals _n_. If there exist multiple solutions for _y_, then any one of those solutions will suffice. However, _y_ must be in sorted order. You can assume that _n_ will be an integer greater than 5.\r\n\r\n","description_html":"\u003cp\u003eGoldbach's strong conjecture states that every even integer greater than 2 can be expressed as the sum of two primes. For example: 4 = 2+2, 6 = 3+3, 8 = 3+5, 10 = 3+7 = 5+5, 12 = 5+7 etc.\u003c/p\u003e\u003cp\u003eAs a corrollary, Goldbach's weak conjecture states that every odd integer greater than 7 can be expressed as the sum of three odd primes. For example: 9 = 3+3+3, 11 = 3+3+5, 13 = 3+3+7 = 3+5+5, 15 = 3+5+7 = 5+5+5 etc.\u003c/p\u003e\u003cp\u003eA third conjecture was written by Goldbach in the margin of a letter, and (in its modern version) states that\u003c/p\u003e\u003cp\u003e\" \u003ci\u003eEvery integer greater than 5 can be expressed as the sum of three primes.\u003c/i\u003e \"\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cul\u003e\u003cli\u003e6 = 2 + 2 + 2\u003c/li\u003e\u003cli\u003e7 = 2 + 2 + 3\u003c/li\u003e\u003cli\u003e8 = 2 + 3 + 3\u003c/li\u003e\u003cli\u003e9 = 2 + 2 + 5 = 3 + 3 + 3\u003c/li\u003e\u003cli\u003e10 = 2 + 3 + 5\u003c/li\u003e\u003cli\u003e11 = 2 + 2 + 7 = 3 + 3 + 5\u003c/li\u003e\u003cli\u003e12 = 2 + 3 + 7 = 2 + 5 + 5\u003c/li\u003e\u003cli\u003e13 = 3 + 3 + 7 = 3 + 5 + 5\u003c/li\u003e\u003cli\u003e14 = 2 + 5 + 7\u003c/li\u003e\u003cli\u003e15 = 2 + 2 + 11 = 3 + 5 + 7 = 5 + 5 + 5\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eYour task is to write a function which takes a positive integer \u003ci\u003en\u003c/i\u003e as input, and which returns a 1-by-3 vector \u003ci\u003ey\u003c/i\u003e, which contains three numbers that are primes and whose sum equals \u003ci\u003en\u003c/i\u003e. If there exist multiple solutions for \u003ci\u003ey\u003c/i\u003e, then any one of those solutions will suffice. However, \u003ci\u003ey\u003c/i\u003e must be in sorted order. You can assume that \u003ci\u003en\u003c/i\u003e will be an integer greater than 5.\u003c/p\u003e","function_template":"function y = goldbach3(n)\r\n  y = [n,n,n];\r\nend","test_suite":"%%\r\nn = 6;\r\ny = goldbach3(n);\r\ny_correct = [2,2,2];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 7;\r\ny = goldbach3(n);\r\ny_correct = [2,2,3];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 8;\r\ny = goldbach3(n);\r\ny_correct = [2,3,3];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 9;\r\ny = goldbach3(n);\r\ny_correct1 = [2,2,5];\r\ny_correct2 = [3,3,3];\r\nassert(isequal(y,y_correct1)|isequal(y,y_correct2))\r\n\r\n%%\r\nn = 10;\r\ny = goldbach3(n);\r\ny_correct = [2,3,5];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 11;\r\ny = goldbach3(n);\r\ny_correct1 = [2,2,7];\r\ny_correct2 = [3,3,5];\r\nassert(isequal(y,y_correct1)|isequal(y,y_correct2))\r\n\r\n%%\r\nn = 12;\r\ny = goldbach3(n);\r\ny_correct1 = [2,3,7];\r\ny_correct2 = [2,5,5];\r\nassert(isequal(y,y_correct1)|isequal(y,y_correct2))\r\n\r\n%%\r\nn = 13;\r\ny = goldbach3(n);\r\ny_correct1 = [3,3,7];\r\ny_correct2 = [3,5,5];\r\nassert(isequal(y,y_correct1)|isequal(y,y_correct2))\r\n\r\n%%\r\nn = 14;\r\ny = goldbach3(n);\r\ny_correct = [2,5,7];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 15;\r\ny = goldbach3(n);\r\ny_correct1 = [2,2,11];\r\ny_correct2 = [3,5,7];\r\ny_correct3 = [5,5,5];\r\nassert(isequal(y,y_correct1)|isequal(y,y_correct2)|isequal(y,y_correct3))\r\n\r\n%%\r\nn = 101;\r\ny = goldbach3(n);\r\nassert(isequal(y,sort(y)))\r\nassert(all(isprime(y)))\r\nassert(sum(y)==n)\r\n\r\n%%\r\nn = 102;\r\ny = goldbach3(n);\r\nassert(isequal(y,sort(y)))\r\nassert(all(isprime(y)))\r\nassert(sum(y)==n)\r\n\r\n%% \r\nfor n = 250:300\r\n    y = goldbach3(n);\r\n    assert(isequal(y,sort(y)));\r\n    assert(all(isprime(y)));\r\n    assert(sum(y)==n);\r\nend\r\n\r\n%%\r\nn = randi(2000)+5; % generate a random integer greater than 5 and smaller than 2006\r\ny = goldbach3(n);\r\nassert(isequal(y,sort(y)))\r\nassert(all(isprime(y)))\r\nassert(sum(y)==n)\r\n\r\n%% \r\nvalid = zeros(1,50);\r\nfor k = 1:50\r\n    n = randi(1000)+5; % generate a random integer greater than 5 and smaller than 1006\r\n    yk = goldbach3(n);\r\n    valid(k) = (isequal(yk,sort(yk)) \u0026 all(isprime(yk)) \u0026 sum(yk)==n);\r\nend\r\nassert(all(valid));\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":108199,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":76,"test_suite_updated_at":"2017-11-18T23:12:48.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-11-14T00:05:38.000Z","updated_at":"2026-04-15T01:39:36.000Z","published_at":"2017-11-14T01:21:48.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGoldbach's strong conjecture states that every even integer greater than 2 can be expressed as the sum of two primes. For example: 4 = 2+2, 6 = 3+3, 8 = 3+5, 10 = 3+7 = 5+5, 12 = 5+7 etc.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs a corrollary, Goldbach's weak conjecture states that every odd integer greater than 7 can be expressed as the sum of three odd primes. For example: 9 = 3+3+3, 11 = 3+3+5, 13 = 3+3+7 = 3+5+5, 15 = 3+5+7 = 5+5+5 etc.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA third conjecture was written by Goldbach in the margin of a letter, and (in its modern version) states that\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEvery integer greater than 5 can be expressed as the sum of three primes.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e6 = 2 + 2 + 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e7 = 2 + 2 + 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e8 = 2 + 3 + 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e9 = 2 + 2 + 5 = 3 + 3 + 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e10 = 2 + 3 + 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e11 = 2 + 2 + 7 = 3 + 3 + 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e12 = 2 + 3 + 7 = 2 + 5 + 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e13 = 3 + 3 + 7 = 3 + 5 + 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e14 = 2 + 5 + 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e15 = 2 + 2 + 11 = 3 + 5 + 7 = 5 + 5 + 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task is to write a function which takes a positive integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as input, and which returns a 1-by-3 vector\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which contains three numbers that are primes and whose sum equals\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. If there exist multiple solutions for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, then any one of those solutions will suffice. However,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e must be in sorted order. You can assume that\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be an integer greater than 5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2910,"title":"Mersenne Primes vs. All Primes","description":"A Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number. \u003chttps://www.mathworks.com/matlabcentral/cody/problems/525-mersenne-primes Problem 525\u003e asks the user to determine if a number is a Mersenne prime. In this problem, you are tasked with returning the number of primes numbers below the input number, n, that are Mersenne primes and the fraction of all primes below that input number that the Mersenne primes represent.\r\n\r\nFor example, for n = 100, there are 25 primes numbers: 2, 3, 5, 7, ..., 89, 97. As far as Mersenne primes go, there are only three that are less than 100: 2^2 - 1 = 3, 2^3 - 1 = 7, and 2^5 - 1 = 31. The corresponding fraction would be 3/25.","description_html":"\u003cp\u003eA Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number. \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/525-mersenne-primes\"\u003eProblem 525\u003c/a\u003e asks the user to determine if a number is a Mersenne prime. In this problem, you are tasked with returning the number of primes numbers below the input number, n, that are Mersenne primes and the fraction of all primes below that input number that the Mersenne primes represent.\u003c/p\u003e\u003cp\u003eFor example, for n = 100, there are 25 primes numbers: 2, 3, 5, 7, ..., 89, 97. As far as Mersenne primes go, there are only three that are less than 100: 2^2 - 1 = 3, 2^3 - 1 = 7, and 2^5 - 1 = 31. The corresponding fraction would be 3/25.\u003c/p\u003e","function_template":"function [y,f] = Mersenne_prime_comp(n)\r\n y = 1;\r\n f = 0;\r\nend","test_suite":"%%\r\nn = 1e2;\r\ny_correct = 3;\r\nf_correct = 3/25;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(isequal(f,f_correct))\r\n\r\n%%\r\nn = 1e3;\r\ny_correct = 4;\r\nf_correct = 0.023809523809524;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n\r\n%%\r\nn = 1e4;\r\ny_correct = 5;\r\nf_correct = 0.004068348250610;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n\r\n%%\r\nn = 1e5;\r\ny_correct = 5;\r\nf_correct = 5.212677231025855e-04;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n\r\n%%\r\nn = 1e6;\r\ny_correct = 7;\r\nf_correct = 8.917424647761727e-05;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n","published":true,"deleted":false,"likes_count":8,"comments_count":2,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":849,"test_suite_updated_at":"2015-02-01T04:14:08.000Z","rescore_all_solutions":false,"group_id":29,"created_at":"2015-02-01T03:56:07.000Z","updated_at":"2026-05-06T01:12:18.000Z","published_at":"2015-02-01T04:14:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/525-mersenne-primes\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 525\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asks the user to determine if a number is a Mersenne prime. In this problem, you are tasked with returning the number of primes numbers below the input number, n, that are Mersenne primes and the fraction of all primes below that input number that the Mersenne primes represent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, for n = 100, there are 25 primes numbers: 2, 3, 5, 7, ..., 89, 97. As far as Mersenne primes go, there are only three that are less than 100: 2^2 - 1 = 3, 2^3 - 1 = 7, and 2^5 - 1 = 31. The corresponding fraction would be 3/25.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2595,"title":"Polite numbers. Politeness.","description":"A polite number is an integer that sums of two or more consecutive positive integers.\r\nPoliteness of a positive integer is a number of nontrivial ways to write n as a sum of two or more consecutive positive integers.\r\n\r\nFor example _9 = 4+5 = 2+3+4_  and politeness of 9 is 2.\r\n\r\nGiven _N_ return politeness of _N_.\r\n\r\nSee also \u003chttp://www.mathworks.co.uk/matlabcentral/cody/problems/2593 2593\u003e","description_html":"\u003cp\u003eA polite number is an integer that sums of two or more consecutive positive integers.\r\nPoliteness of a positive integer is a number of nontrivial ways to write n as a sum of two or more consecutive positive integers.\u003c/p\u003e\u003cp\u003eFor example \u003ci\u003e9 = 4+5 = 2+3+4\u003c/i\u003e  and politeness of 9 is 2.\u003c/p\u003e\u003cp\u003eGiven \u003ci\u003eN\u003c/i\u003e return politeness of \u003ci\u003eN\u003c/i\u003e.\u003c/p\u003e\u003cp\u003eSee also \u003ca href = \"http://www.mathworks.co.uk/matlabcentral/cody/problems/2593\"\u003e2593\u003c/a\u003e\u003c/p\u003e","function_template":"function P = politeness(N)\r\n  P=N;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 2;\r\ny_correct = 0;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 3;\r\ny_correct = 1;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 7;\r\ny_correct = 1;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 9;\r\ny_correct = 2;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 15;\r\ny_correct = 3;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 18;\r\ny_correct = 2;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 21;\r\ny_correct = 3;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 1024;\r\ny_correct = 0;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 1025;\r\ny_correct = 5;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 25215;\r\ny_correct = 11;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 62;\r\ny_correct = 1;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 63;\r\ny_correct = 5;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 65;\r\ny_correct = 3;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\n% anti-lookup \u0026 clue\r\nnums=primes(200);\r\npattern=[1 nums([false ~randi([0 25],1,45)])];\r\nx=prod(pattern)*2^randi([0 5]);\r\ny_correct=2^numel(pattern)/2-1;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nfor k=randi(2e4,1,20)\r\n  assert(isequal(politeness(k*(k-1))+1,(politeness(k)+1)*(politeness(k-1)+1)))\r\nend","published":true,"deleted":false,"likes_count":8,"comments_count":6,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":189,"test_suite_updated_at":"2014-09-17T15:38:21.000Z","rescore_all_solutions":false,"group_id":8,"created_at":"2014-09-16T22:47:12.000Z","updated_at":"2026-05-05T05:28:08.000Z","published_at":"2014-09-17T10:56:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA polite number is an integer that sums of two or more consecutive positive integers. Politeness of a positive integer is a number of nontrivial ways to write n as a sum of two or more consecutive positive integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e9 = 4+5 = 2+3+4\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and politeness of 9 is 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e return politeness of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.co.uk/matlabcentral/cody/problems/2593\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e2593\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1672,"title":"Leftovers?  Again?!","description":"I am thinking of a positive number X.  To determine what number I am thinking of, I will give you two 1xN vectors.  The first vector (V1) is several numbers, none of which will share a factor.  The second vector (V2) is the remainder of X when divided by each of the numbers in V1. Calculate what the lowest possible value of X can be given these criteria.  For example:\r\n\r\nV1 = [2 3] ; V2 = [1 2]\r\n\r\nwould give an X value of 5.  There are an infinite number of other values of X that would satisfy V1 and V2, but I want the lowest one.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 82.5px; vertical-align: baseline; perspective-origin: 332px 82.5px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 42px; white-space: pre-wrap; perspective-origin: 309px 42px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eI am thinking of a positive number X. To determine what number I am thinking of, I will give you two 1xN vectors. The first vector (V1) is several numbers, none of which will share a factor. The second vector (V2) is the remainder of X when divided by each of the numbers in V1. Calculate what the lowest possible value of X can be given these criteria. For example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eV1 = [2 3] ; V2 = [1 2]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewould give an X value of 5. There are an infinite number of other values of X that would satisfy V1 and V2, but I want the lowest one.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function X = leftovers(n,a)\r\n X = pi;\r\nend","test_suite":"%!cp leftovers.m safe\r\n%!rm *.*\r\n%!mv safe leftovers.m\r\n%!rm @*\r\n\r\n% Clean user's function from some known jailbreaking mechanisms\r\nfid = fopen('leftovers.m');\r\nst = regexprep(char(fread(fid)'), '!', 'error(''No shell commands!''); %');\r\nst = regexprep(st, 'feval', 'error(''No fancy functions!''); %');\r\nst = regexprep(st, 'str2func', 'error(''No fancy functions!''); %');\r\nst = regexprep(st, 'regex', 'error(''No fancy functions!''); %');\r\nst = regexprep(st, 'system', 'error(''No shell commands!''); %');\r\nst = regexprep(st, 'dos', 'error(''No shell commands!''); %');\r\nst = regexprep(st, 'unix', 'error(''No shell commands!''); %');\r\nst = regexprep(st, 'perl', 'error(''No external languages commands!''); %');\r\nst = regexprep(st, 'java', 'error(''No external languages commands!''); %');\r\nst = regexprep(st, 'assert', 'error(''No overwriting!''); %');\r\nfclose(fid)\r\n\r\nfid = fopen('leftovers.m' , 'w');\r\nfwrite(fid,st);\r\nfclose(fid)\r\n%%\r\nV1 = [2 3] ; V2 = [1 2];; y_correct = 5; assert(isequal(leftovers(V1,V2),y_correct))\r\n%%\r\nV1=[3 5 7] ; V2=[1 2 3]; y_correct = 52; assert(isequal(leftovers(V1,V2),y_correct))\r\n%%\r\nV1=[3 4 5] ; V2=[2 3 1]; y_correct = 11; assert(isequal(leftovers(V1,V2),y_correct))\r\n%%\r\nV1=[4 9 25] ; V2=[3 2 7]; y_correct = 407; assert(isequal(leftovers(V1,V2),y_correct))\r\n%%\r\nV1=[9 10 77] ; V2=[1 2 69]; y_correct = 6922; assert(isequal(leftovers(V1,V2),y_correct))\r\n%%\r\na=primes(30);\r\nb=ceil(8*rand()+2)\r\nV1=a(1:b);V2=1:b;\r\ny_correct=[23 53 1523 29243 299513 4383593 188677703 5765999453];\r\nassert(isequal(leftovers(V1,V2),y_correct(b-2)))\r\n%%\r\nV1=[leftovers([6 35],[3 9]) leftovers([3 5 7],[1 3 1])];\r\nassert(isequal(leftovers(V1,V1-8),379))\r\n%%\r\n% Discourage the for x=1:inf loops\r\nV1=[74 93 145 161 209 221]; V2=[66 85 137 153 201 213];\r\ny_correct=7420738134802;\r\nassert(isequal(leftovers(V1,V2),y_correct))\r\n%%\r\n% Discourage the for x=1:inf loops\r\nV1=[17 82 111 155 203 247 253] ; V2=[11 50 68 95 124 150 154];\r\ny_correct=59652745309190;\r\nassert(isequal(leftovers(V1,V2),y_correct))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":10,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":32,"test_suite_updated_at":"2020-09-29T13:24:49.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-06-21T18:45:36.000Z","updated_at":"2025-11-22T17:35:45.000Z","published_at":"2013-06-21T18:45:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI am thinking of a positive number X. To determine what number I am thinking of, I will give you two 1xN vectors. The first vector (V1) is several numbers, none of which will share a factor. The second vector (V2) is the remainder of X when divided by each of the numbers in V1. Calculate what the lowest possible value of X can be given these criteria. For example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eV1 = [2 3] ; V2 = [1 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewould give an X value of 5. There are an infinite number of other values of X that would satisfy V1 and V2, but I want the lowest one.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60,"title":"The Goldbach Conjecture","description":"The Goldbach conjecture asserts that every even integer greater than 2 can be expressed as the sum of two primes.\r\nGiven the even integer n, return primes p1 and p2 that satisfy the condition n = p1 + p2. Note that the primes are not always unique. The test is not sensitive to order or uniqueness. You just need to meet the appropriate conditions.\r\nExample:\r\n Input  n = 286\r\n Output (any of the following is acceptable) \r\n        [  3 283]\r\n        [283   3]\r\n        [  5 281]\r\n        [107 179]\r\n        [137 149]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 255.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 127.517px; transform-origin: 407px 127.517px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.5px 8px; transform-origin: 12.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eGoldbach conjecture\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 287px 8px; transform-origin: 287px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asserts that every even integer greater than 2 can be expressed as the sum of two primes.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.5px 8px; transform-origin: 368.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the even integer n, return primes p1 and p2 that satisfy the condition n = p1 + p2. Note that the primes are not always unique. The test is not sensitive to order or uniqueness. You just need to meet the appropriate conditions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.5px 8px; transform-origin: 28.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 143.033px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 71.5167px; transform-origin: 404px 71.5167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 60px 8.5px; tab-size: 4; transform-origin: 60px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003e Input  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 28px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 28px 8.5px; \"\u003en = 286\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 180px 8.5px; tab-size: 4; transform-origin: 180px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e Output (any of the following is acceptable) \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        [  3 283]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        [283   3]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        [  5 281]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        [107 179]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        [137 149]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [p1,p2] = goldbach(n)\r\n  p1 = n;\r\n  p2 = n;\r\nend","test_suite":"%%\r\nfiletext = fileread('goldbach.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)\r\n\r\n%%\r\nnList = 28:6:76;\r\nfor i = 1:length(nList)\r\n  n = nList(i);\r\n  [p1,p2] = goldbach(n)\r\n  assert(isprime(p1) \u0026\u0026 isprime(p2) \u0026\u0026 (p1+p2==n));\r\nend\r\n\r\n%%\r\nnList = [18 20 22 100 102 114 1000 2000 36 3600];\r\nfor i = 1:length(nList)\r\n  n = nList(i);\r\n  [p1,p2] = goldbach(n)\r\n  assert(isprime(p1) \u0026\u0026 isprime(p2) \u0026\u0026 (p1+p2==n));\r\nend","published":true,"deleted":false,"likes_count":60,"comments_count":17,"created_by":1,"edited_by":223089,"edited_at":"2023-06-05T15:48:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5982,"test_suite_updated_at":"2023-06-05T15:48:22.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:25.000Z","updated_at":"2026-05-08T20:48:29.000Z","published_at":"2012-01-18T01:00:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGoldbach conjecture\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asserts that every even integer greater than 2 can be expressed as the sum of two primes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the even integer n, return primes p1 and p2 that satisfy the condition n = p1 + p2. Note that the primes are not always unique. The test is not sensitive to order or uniqueness. You just need to meet the appropriate conditions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input  n = 286\\n Output (any of the following is acceptable) \\n        [  3 283]\\n        [283   3]\\n        [  5 281]\\n        [107 179]\\n        [137 149]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":64,"title":"The Goldbach Conjecture, Part 2","description":"The \u003chttp://en.wikipedia.org/wiki/Goldbach's_conjecture Goldbach\nconjecture\u003e asserts that every even integer greater than 2 can be\nexpressed as the sum of two primes.\n \nGiven the even integer n, return c, the number of different ways two primes can be added to result in n. Only count a pair once; the order is unimportant.\n\nExample:\n\n Input  n = 10\n Output c is 2\n\nbecause of the prime pairs [3 7] and [5 5].\n\n Input  n = 50\n Output c is 4\n\nbecause of [3 47], [7 43], [13 37], and [19 31].\n","description_html":"\u003cp\u003eThe \u003ca href=\"http://en.wikipedia.org/wiki/Goldbach's_conjecture\"\u003eGoldbach\nconjecture\u003c/a\u003e asserts that every even integer greater than 2 can be\nexpressed as the sum of two primes.\u003c/p\u003e\u003cp\u003eGiven the even integer n, return c, the number of different ways two primes can be added to result in n. Only count a pair once; the order is unimportant.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e Input  n = 10\n Output c is 2\u003c/pre\u003e\u003cp\u003ebecause of the prime pairs [3 7] and [5 5].\u003c/p\u003e\u003cpre\u003e Input  n = 50\n Output c is 4\u003c/pre\u003e\u003cp\u003ebecause of [3 47], [7 43], [13 37], and [19 31].\u003c/p\u003e","function_template":"function c = goldbach2(n)\n  c = 1;\nend","test_suite":"%%\nn = 6;\nc_correct = 1;\nassert(isequal(goldbach2(n),c_correct))\n\n%%\nn = 10;\nc_correct = 2;\nassert(isequal(goldbach2(n),c_correct))\n\n%%\nn = 50;\nc_correct = 4;\nassert(isequal(goldbach2(n),c_correct))\n\n%%\nn = 480;\nc_correct = 29;\nassert(isequal(goldbach2(n),c_correct))","published":true,"deleted":false,"likes_count":18,"comments_count":4,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2417,"test_suite_updated_at":"2012-01-18T01:00:26.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:26.000Z","updated_at":"2026-05-05T20:42:32.000Z","published_at":"2012-01-18T01:00:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Goldbach's_conjecture\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGoldbach conjecture\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asserts that every even integer greater than 2 can be expressed as the sum of two primes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the even integer n, return c, the number of different ways two primes can be added to result in n. Only count a pair once; the order is unimportant.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input  n = 10\\n Output c is 2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ebecause of the prime pairs [3 7] and [5 5].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input  n = 50\\n Output c is 4]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ebecause of [3 47], [7 43], [13 37], and [19 31].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":83,"title":"Prime factor digits","description":"Consider the following number system. Calculate the prime factorization for each number n, then represent the prime factors in a vector like so:\r\n       13 11 7 5 3 2\r\n      ---------------\r\n    2:             1\r\n    3:           1 0\r\n    4:             2\r\n    5:         1 0 0\r\n    6:           1 1\r\n   12:           1 2\r\n   14:       1 0 0 1\r\n   18:           2 1\r\n   26:   1 0 0 0 0 1\r\n   60:         1 1 2\r\nEach \"place\" in the number system represents a prime number. Given n, return the vector p.\r\nAs shown above, if n = 26, then p = [1 0 0 0 0 1].\r\nThe input n is always an integer greater than 1. Suppress any leading zeros. The length of the vector is determined by the largest prime factor.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 409.2px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 204.6px; transform-origin: 407px 204.6px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.5px 8px; transform-origin: 368.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider the following number system. Calculate the prime factorization for each number n, then represent the prime factors in a vector like so:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 245.2px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 122.6px; transform-origin: 404px 122.6px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e       13 11 7 5 3 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 84px 8.5px; transform-origin: 84px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e      ---------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    2:             1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    3:           1 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    4:             2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    5:         1 0 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    6:           1 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   12:           1 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   14:       1 0 0 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   18:           2 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   26:   1 0 0 0 0 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   60:         1 1 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 289.5px 8px; transform-origin: 289.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach \"place\" in the number system represents a prime number. Given n, return the vector p.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 153px 8px; transform-origin: 153px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs shown above, if n = 26, then p = [1 0 0 0 0 1].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe input n is always an integer greater than 1. Suppress any leading zeros. The length of the vector is determined by the largest prime factor.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = factor_digits(n)\r\n  p = 0;\r\nend","test_suite":"%%\r\nn = 26;\r\np_correct = [1 0 0 0 0 1];\r\nassert(isequal(factor_digits(n),p_correct))\r\n\r\n%%\r\nn = 168;\r\np_correct = [1 0 1 3];\r\nassert(isequal(factor_digits(n),p_correct))\r\n\r\n%%\r\nn = 2;\r\np_correct = 1;\r\nassert(isequal(factor_digits(n),p_correct))\r\n\r\n%%\r\nn = 1444;\r\np_correct = 2*[1 0 0 0 0 0 0 1];\r\nassert(isequal(factor_digits(n),p_correct))\r\n\r\n%%\r\nn = 47;\r\np_correct = [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0];\r\nassert(isequal(factor_digits(n),p_correct))\r\n\r\n%%\r\nn = 999;\r\np_correct = [1 0 0 0 0 0 0 0 0 0 3 0];\r\nassert(isequal(factor_digits(n),p_correct))\r\n\r\n%%\r\nn = 20;\r\np_correct = [1 0 2];\r\nassert(isequal(factor_digits(n),p_correct))","published":true,"deleted":false,"likes_count":28,"comments_count":6,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2543,"test_suite_updated_at":"2021-08-08T11:30:25.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:29.000Z","updated_at":"2026-05-05T20:56:35.000Z","published_at":"2012-01-18T01:00:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the following number system. Calculate the prime factorization for each number n, then represent the prime factors in a vector like so:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[       13 11 7 5 3 2\\n      ---------------\\n    2:             1\\n    3:           1 0\\n    4:             2\\n    5:         1 0 0\\n    6:           1 1\\n   12:           1 2\\n   14:       1 0 0 1\\n   18:           2 1\\n   26:   1 0 0 0 0 1\\n   60:         1 1 2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach \\\"place\\\" in the number system represents a prime number. Given n, return the vector p.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs shown above, if n = 26, then p = [1 0 0 0 0 1].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe input n is always an integer greater than 1. Suppress any leading zeros. The length of the vector is determined by the largest prime factor.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1095,"title":"Circular Primes (based on Project Euler, problem 35)","description":"The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.\r\n\r\nThere are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.\r\n\r\nGiven a number x, write a MATLAB script that will tell you the number of circular primes less than or equal to x as well as a sorted list of what the circular prime numbers are.","description_html":"\u003cp\u003eThe number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.\u003c/p\u003e\u003cp\u003eThere are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.\u003c/p\u003e\u003cp\u003eGiven a number x, write a MATLAB script that will tell you the number of circular primes less than or equal to x as well as a sorted list of what the circular prime numbers are.\u003c/p\u003e","function_template":"function [how_many what_numbers]=circular_prime(x)\r\n    how_many=3;\r\n    what_numbers=[2 3 5];\r\nend","test_suite":"%%\r\n[y numbers]=circular_prime(197)\r\nassert(isequal(y,16)\u0026\u0026isequal(numbers,[2 3 5 7 11 13 17 31 37 71 73 79 97 113 131 197]))\r\n%%\r\n[y numbers]=circular_prime(100)\r\nassert(isequal(y,13)\u0026\u0026isequal(numbers,[2 3 5 7 11 13 17 31 37 71 73 79 97]))\r\n%%\r\n[y numbers]=circular_prime(250)\r\nassert(isequal(y,17)\u0026\u0026isequal(numbers,[2 3 5 7 11 13 17 31 37 71 73 79 97 113 131 197 199]))\r\n%%\r\n[y numbers]=circular_prime(2000)\r\nassert(isequal(y,27)\u0026\u0026isequal(numbers,[2 3 5 7 11 13 17 31 37 71 73 79 97 113 131 197 199 311 337 373 719 733 919 971 991 1193 1931]))\r\n%%\r\n[y numbers]=circular_prime(10000)\r\nassert(isequal(y,33)\u0026\u0026isequal(numbers,[2 3 5 7 11 13 17 31 37 71 73 79 97 113 131 197 199 311 337 373 719 733 919 971 991 1193 1931 3119 3779 7793 7937 9311 9377]))\r\n%%\r\n[y numbers]=circular_prime(54321)\r\nassert(isequal(y,38)\u0026\u0026isequal(numbers,[2 3 5 7 11 13 17 31 37 71 73 79 97 113 131 197 199 311 337 373 719 733 919 971 991 1193 1931 3119 3779 7793 7937 9311 9377 11939 19391 19937 37199 39119]))\r\n","published":true,"deleted":false,"likes_count":10,"comments_count":6,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":655,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-12-05T18:02:09.000Z","updated_at":"2026-05-06T03:26:47.000Z","published_at":"2012-12-05T18:02:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a number x, write a MATLAB script that will tell you the number of circular primes less than or equal to x as well as a sorted list of what the circular prime numbers are.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":2736,"title":"Pernicious Anniversary Problem","description":"Since Cody is 5 years old, it's pernicious. A \u003chttp://rosettacode.org/wiki/Pernicious_numbers Pernicious number\u003e is an integer whose population count is a prime. Check if the given number is pernicious.","description_html":"\u003cp\u003eSince Cody is 5 years old, it's pernicious. A \u003ca href = \"http://rosettacode.org/wiki/Pernicious_numbers\"\u003ePernicious number\u003c/a\u003e is an integer whose population count is a prime. Check if the given number is pernicious.\u003c/p\u003e","function_template":"function y = isPernicious(x)\r\n  y = false;\r\nend","test_suite":"%%\r\nx = 5;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 1;\r\ny_correct = false;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 2^randi(16);\r\ny_correct = false;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 17;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 18;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 61;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 6;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 2115;\r\ny_correct = false;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 2114;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n%%\r\nx = 2017;\r\ny_correct = true;\r\nassert(isequal(isPernicious(x),y_correct))\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":13,"comments_count":1,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":840,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":34,"created_at":"2014-12-08T08:48:45.000Z","updated_at":"2026-05-03T23:00:10.000Z","published_at":"2017-10-16T01:45:06.000Z","restored_at":"2017-10-25T14:37:50.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince Cody is 5 years old, it's pernicious. A\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://rosettacode.org/wiki/Pernicious_numbers\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePernicious number\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer whose population count is a prime. Check if the given number is pernicious.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":248,"title":"Twins in a Window","description":"\u003chttp://en.wikipedia.org/wiki/Twin_primes Twin primes\u003e are prime numbers that differ by 2, such as [11,13] or [41,43]. Write a function that returns a sorted list of the twin primes between lowVal and highVal (all the primes must be greater than lowVal and less than highVal). The primes should be arranged in an n-by-2 matrix as shown in the examples below.\r\n\r\nExamples:\r\n\r\n Input  lowVal = 10, highVal = 50\r\n Output p is [ 11    13\r\n               17    19\r\n               29    31\r\n               41    43 ]\r\n\r\n Input  lowVal = 1000, highVal = 1050\r\n Output p is [ 1019  1021\r\n               1031  1033 ]\r\n","description_html":"\u003cp\u003e\u003ca href=\"http://en.wikipedia.org/wiki/Twin_primes\"\u003eTwin primes\u003c/a\u003e are prime numbers that differ by 2, such as [11,13] or [41,43]. Write a function that returns a sorted list of the twin primes between lowVal and highVal (all the primes must be greater than lowVal and less than highVal). The primes should be arranged in an n-by-2 matrix as shown in the examples below.\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cpre\u003e Input  lowVal = 10, highVal = 50\r\n Output p is [ 11    13\r\n               17    19\r\n               29    31\r\n               41    43 ]\u003c/pre\u003e\u003cpre\u003e Input  lowVal = 1000, highVal = 1050\r\n Output p is [ 1019  1021\r\n               1031  1033 ]\u003c/pre\u003e","function_template":"function p = window_twins(lowVal,highVal)\r\n  p = 0;\r\nend","test_suite":"%%\r\nlowVal = 10;\r\nhighVal = 50;\r\np = [11    13\r\n     17    19\r\n     29    31\r\n     41    43];\r\nassert(isequal(window_twins(lowVal,highVal),p))\r\n\r\n%%\r\nlowVal = 1000;\r\nhighVal = 1050;\r\np = [1019  1021\r\n     1031  1033];\r\nassert(isequal(window_twins(lowVal,highVal),p))\r\n\r\n%%\r\nlowVal = 3120;\r\nhighVal = 3300;\r\np = [ 3167  3169\r\n      3251  3253\r\n      3257  3259];\r\nassert(isequal(window_twins(lowVal,highVal),p))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":7,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":162,"test_suite_updated_at":"2012-02-03T17:12:57.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-03T16:30:52.000Z","updated_at":"2026-04-10T14:29:19.000Z","published_at":"2012-02-03T17:12:56.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Twin_primes\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eTwin primes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e are prime numbers that differ by 2, such as [11,13] or [41,43]. Write a function that returns a sorted list of the twin primes between lowVal and highVal (all the primes must be greater than lowVal and less than highVal). The primes should be arranged in an n-by-2 matrix as shown in the examples below.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input  lowVal = 10, highVal = 50\\n Output p is [ 11    13\\n               17    19\\n               29    31\\n               41    43 ]\\n\\n Input  lowVal = 1000, highVal = 1050\\n Output p is [ 1019  1021\\n               1031  1033 ]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44230,"title":"I'm going to enjoy watching you calculate, Mr Anderson","description":"Smith numbers are numbers such that if you add up all of the digits in the number, that sum equals the sum of all of the digits in all of their factors. This term was coined by Albert Wilansky, when he noticed the defining property in the phone number of his brother-in-law Harold Smith: 493-7775.\r\n4+9+3+7+7+7+5=42\r\nThe prime factors of 4937775 are 3, 5, 5, and 65837. 3+5+5+(6+5+8+3+7) = 42\r\nSince all prime numbers obviously meet this criteria, Smith numbers are defined as composite numbers. Write a MATLAB function that will tell you if a given number is a Smith number.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 174px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 87px; transform-origin: 407px 87px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.5px 8px; transform-origin: 375.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSmith numbers are numbers such that if you add up all of the digits in the number, that sum equals the sum of all of the digits in all of their factors. This term was coined by Albert Wilansky, when he noticed the defining property in the phone number of his brother-in-law Harold Smith: 493-7775.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64px 8px; transform-origin: 64px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4+9+3+7+7+7+5=42\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 251px 8px; transform-origin: 251px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe prime factors of 4937775 are 3, 5, 5, and 65837. 3+5+5+(6+5+8+3+7) = 42\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.5px 8px; transform-origin: 380.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSince all prime numbers obviously meet this criteria, Smith numbers are defined as composite numbers. Write a MATLAB function that will tell you if a given number is a Smith number.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = smith(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nassert(isequal(smith(4937775),1))\r\n%%\r\nassert(isequal(smith(1164),0))\r\n%%\r\nassert(isequal(smith(19683),1))\r\n%%\r\nassert(isequal(smith(11),0))  % Remember - Smith numbers are composite\r\n%%\r\nassert(isequal(smith(11^2),1))\r\n%%\r\nassert(isequal(smith(345741),1))\r\n%%\r\nassert(isequal(smith(19876),0))\r\n%%\r\nassert(isequal(smith(314159),0))\r\n%%\r\nassert(isequal(smith(612985),1))\r\n%%\r\nassert(isequal(smith(12379887),1))\r\n%%\r\nassert(isequal(smith(23456789),0))\r\n%%\r\nassert(isequal(smith(13),0))\r\n%%\r\nassert(isequal(smith(23),0))\r\n%%\r\ny=primes(randi(1e5));\r\nassert(isequal(smith(y(end)),0))\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":1615,"edited_by":223089,"edited_at":"2023-01-07T08:26:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":49,"test_suite_updated_at":"2023-01-07T08:26:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-06-01T19:16:25.000Z","updated_at":"2026-03-16T15:29:16.000Z","published_at":"2017-06-01T19:16:25.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSmith numbers are numbers such that if you add up all of the digits in the number, that sum equals the sum of all of the digits in all of their factors. This term was coined by Albert Wilansky, when he noticed the defining property in the phone number of his brother-in-law Harold Smith: 493-7775.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e4+9+3+7+7+7+5=42\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe prime factors of 4937775 are 3, 5, 5, and 65837. 3+5+5+(6+5+8+3+7) = 42\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince all prime numbers obviously meet this criteria, Smith numbers are defined as composite numbers. Write a MATLAB function that will tell you if a given number is a Smith number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44384,"title":"Find the nearest prime number","description":"Happy 5th birthday, Cody! Since 5 is a prime number, let's have some fun looking for other prime numbers.\r\n\r\nGiven a positive integer x, find the nearest prime number. Keep in mind that the nearest prime may be less than x.\r\n\r\n*Examples*\r\n\r\n  nearestprime(5) = 5\r\n  nearestprime(36) = 37\r\n  nearestprime(200) = 199\r\n\r\nNOTE: You may ignore cases in which two prime numbers are equally close to x. (e.g., x=12 --\u003e 11 and 13 are both primes). ","description_html":"\u003cp\u003eHappy 5th birthday, Cody! Since 5 is a prime number, let's have some fun looking for other prime numbers.\u003c/p\u003e\u003cp\u003eGiven a positive integer x, find the nearest prime number. Keep in mind that the nearest prime may be less than x.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003enearestprime(5) = 5\r\nnearestprime(36) = 37\r\nnearestprime(200) = 199\r\n\u003c/pre\u003e\u003cp\u003eNOTE: You may ignore cases in which two prime numbers are equally close to x. (e.g., x=12 --\u0026gt; 11 and 13 are both primes).\u003c/p\u003e","function_template":"function y = nearestprime(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 0;\r\ny_correct = 2;\r\nassert(isequal(nearestprime(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 5;\r\nassert(isequal(nearestprime(x),y_correct))\r\n\r\n%%\r\nx = 100;\r\ny_correct = 101;\r\nassert(isequal(nearestprime(x),y_correct))\r\n\r\n%%\r\nx = 500;\r\ny_correct = 499;\r\nassert(isequal(nearestprime(x),y_correct))\r\n\r\n%%\r\nx = 911;\r\ny_correct = 911;\r\nassert(isequal(nearestprime(x),y_correct))\r\n\r\n%%\r\nx = 2500;\r\ny_correct = 2503;\r\nassert(isequal(nearestprime(x),y_correct))\r\n\r\n%%\r\nx = 8000;\r\ny_correct = 7993;\r\nassert(isequal(nearestprime(x),y_correct))\r\n\r\n%%\r\nx = 100000;\r\ny_correct = 100003;\r\nassert(isequal(nearestprime(x),y_correct))\r\n\r\n%%\r\nx = 1300000;\r\ny_correct = 1299989;\r\nassert(isequal(nearestprime(x),y_correct))\r\n\r\n%%\r\nx = 179424710;\r\ny_correct = 179424719;\r\nassert(isequal(nearestprime(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":9,"comments_count":1,"created_by":4793,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":664,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":34,"created_at":"2017-10-13T19:42:15.000Z","updated_at":"2026-04-07T15:16:58.000Z","published_at":"2017-10-16T01:45:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHappy 5th birthday, Cody! Since 5 is a prime number, let's have some fun looking for other prime numbers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a positive integer x, find the nearest prime number. Keep in mind that the nearest prime may be less than x.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[nearestprime(5) = 5\\nnearestprime(36) = 37\\nnearestprime(200) = 199]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNOTE: You may ignore cases in which two prime numbers are equally close to x. (e.g., x=12 --\u0026gt; 11 and 13 are both primes).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":3016,"title":"Twin Primes","description":"Twin primes are pairs of primes that are immediately next to each other (difference of two). The lesser of twin primes are 3, 5, 11, 17, 29, ... ( \u003chttp://oeis.org/A001359 ref.\u003e ). The greater of twin primes are 5, 7, 13, 19, 31, ... ( \u003chttp://oeis.org/A006512 ref.\u003e ). Therefore, the first five twin primes are [3,5] [5,7] [11,13] [17,19] [29,31].\r\n\r\nFor a given index range n, return the twin primes corresponding to that range as a two-row column array.","description_html":"\u003cp\u003eTwin primes are pairs of primes that are immediately next to each other (difference of two). The lesser of twin primes are 3, 5, 11, 17, 29, ... ( \u003ca href = \"http://oeis.org/A001359\"\u003eref.\u003c/a\u003e ). The greater of twin primes are 5, 7, 13, 19, 31, ... ( \u003ca href = \"http://oeis.org/A006512\"\u003eref.\u003c/a\u003e ). Therefore, the first five twin primes are [3,5] [5,7] [11,13] [17,19] [29,31].\u003c/p\u003e\u003cp\u003eFor a given index range n, return the twin primes corresponding to that range as a two-row column array.\u003c/p\u003e","function_template":"function [twins] = twin_primes(n)\r\n\r\ntwins = n;\r\n\r\nend","test_suite":"%%\r\nn = 1:5;\r\ntwins_corr = [3, 5, 11, 17, 29; 5, 7, 13, 19, 31];\r\nassert(isequal(twin_primes(n),twins_corr))\r\n\r\n%%\r\nn = 1:10;\r\ntwins_corr = [3, 5, 11, 17, 29, 41, 59, 71, 101, 107; 5, 7, 13, 19, 31, 43, 61, 73, 103, 109];\r\nassert(isequal(twin_primes(n),twins_corr))\r\n\r\n%%\r\nn = 1:25;\r\ntwins_corr = [3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521; 5, 7, 13, 19, 31, 43, 61, 73, 103, 109, 139, 151, 181, 193, 199, 229, 241, 271, 283, 313, 349, 421, 433, 463, 523];\r\nassert(isequal(twin_primes(n),twins_corr))\r\n\r\n%%\r\nn = 1:51;\r\ntwins_corr = [3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481, 1487, 1607; 5, 7, 13, 19, 31, 43, 61, 73, 103, 109, 139, 151, 181, 193, 199, 229, 241, 271, 283, 313, 349, 421, 433, 463, 523, 571, 601, 619, 643, 661, 811, 823, 829, 859, 883, 1021, 1033, 1051, 1063, 1093, 1153, 1231, 1279, 1291, 1303, 1321, 1429, 1453, 1483, 1489, 1609];\r\nassert(isequal(twin_primes(n),twins_corr))\r\n\r\n%%\r\nn = 10:29;\r\ntwins_corr = [107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641; 109, 139, 151, 181, 193, 199, 229, 241, 271, 283, 313, 349, 421, 433, 463, 523, 571, 601, 619, 643];\r\nassert(isequal(twin_primes(n),twins_corr))\r\n\r\n%%\r\nn = 2:8;\r\ntwins_corr = [5, 11, 17, 29, 41, 59, 71; 7, 13, 19, 31, 43, 61, 73];\r\nassert(isequal(twin_primes(n),twins_corr))\r\n\r\n%%\r\nn = 35:42;\r\ntwins_corr = [881, 1019, 1031, 1049, 1061, 1091, 1151, 1229; 883, 1021, 1033, 1051, 1063, 1093, 1153, 1231];\r\nassert(isequal(twin_primes(n),twins_corr))\r\n\r\n%%\r\nn = 34:47;\r\ntwins_corr = [857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427; 859, 883, 1021, 1033, 1051, 1063, 1093, 1153, 1231, 1279, 1291, 1303, 1321, 1429];\r\nassert(isequal(twin_primes(n),twins_corr))\r\n\r\n%%\r\nn = 9:-1:4;\r\ntwins_corr = [101, 71, 59, 41, 29, 17; 103, 73, 61, 43, 31, 19];\r\nassert(isequal(twin_primes(n),twins_corr))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":98,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":30,"created_at":"2015-02-14T03:03:50.000Z","updated_at":"2026-03-16T14:18:09.000Z","published_at":"2015-02-14T03:03:50.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTwin primes are pairs of primes that are immediately next to each other (difference of two). The lesser of twin primes are 3, 5, 11, 17, 29, ... (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://oeis.org/A001359\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eref.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e ). The greater of twin primes are 5, 7, 13, 19, 31, ... (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://oeis.org/A006512\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eref.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e ). Therefore, the first five twin primes are [3,5] [5,7] [11,13] [17,19] [29,31].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a given index range n, return the twin primes corresponding to that range as a two-row column array.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44385,"title":"Extra safe primes","description":"Did you know that the number 5 is the first safe prime? A safe prime is a prime number that can be expressed as 2p+1, where p is also a prime.\r\n\r\nTo celebrate Cody's Five-Year Anniversary, write a function to determine if a positive integer n is a safe prime in which the prime p (such that n=2p+1) is *also a safe prime*.\r\n\r\n*Examples*\r\n\r\n  isextrasafe(5) = false % because 5=2*2+1 and 2 is not a safe prime\r\n  isextrasafe(23) = true % because 23=2*11+1 and 11 is also a safe prime (11=2*5+1)\r\n","description_html":"\u003cp\u003eDid you know that the number 5 is the first safe prime? A safe prime is a prime number that can be expressed as 2p+1, where p is also a prime.\u003c/p\u003e\u003cp\u003eTo celebrate Cody's Five-Year Anniversary, write a function to determine if a positive integer n is a safe prime in which the prime p (such that n=2p+1) is \u003cb\u003ealso a safe prime\u003c/b\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eisextrasafe(5) = false % because 5=2*2+1 and 2 is not a safe prime\r\nisextrasafe(23) = true % because 23=2*11+1 and 11 is also a safe prime (11=2*5+1)\r\n\u003c/pre\u003e","function_template":"function tf = isextrasafe(x)\r\n    tf = false;\r\nend","test_suite":"%%\r\nx = 0;\r\nassert(isequal(isextrasafe(x),false))\r\n\r\n%%\r\nx = 5;\r\nassert(isequal(isextrasafe(x),false))\r\n\r\n%%\r\nx = 7;\r\nassert(isequal(isextrasafe(x),false))\r\n\r\n%%\r\nx = 11;\r\nassert(isequal(isextrasafe(x),true))\r\n\r\n%%\r\nx = 15;\r\nassert(isequal(isextrasafe(x),false))\r\n\r\n%%\r\nx = 23;\r\nassert(isequal(isextrasafe(x),true))\r\n\r\n%%\r\nx = 71;\r\nassert(isequal(isextrasafe(x),false))\r\n\r\n%%\r\nx = 719;\r\nassert(isequal(isextrasafe(x),true))\r\n\r\n%%\r\nx = 2039;\r\nassert(isequal(isextrasafe(x),true))\r\n\r\n%%\r\nx = 2040;\r\nassert(isequal(isextrasafe(x),false))\r\n\r\n%%\r\nx = 5807;\r\nassert(isequal(isextrasafe(x),true))","published":true,"deleted":false,"likes_count":13,"comments_count":4,"created_by":4793,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":759,"test_suite_updated_at":"2017-10-19T17:09:19.000Z","rescore_all_solutions":true,"group_id":34,"created_at":"2017-10-13T20:02:13.000Z","updated_at":"2026-05-05T05:38:20.000Z","published_at":"2017-10-16T01:45:10.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDid you know that the number 5 is the first safe prime? A safe prime is a prime number that can be expressed as 2p+1, where p is also a prime.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo celebrate Cody's Five-Year Anniversary, write a function to determine if a positive integer n is a safe prime in which the prime p (such that n=2p+1) is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ealso a safe prime\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[isextrasafe(5) = false % because 5=2*2+1 and 2 is not a safe prime\\nisextrasafe(23) = true % because 23=2*11+1 and 11 is also a safe prime (11=2*5+1)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1204,"title":"Prime Time","description":"All you need to do here is submit your solution a prime number of seconds after the top of the hour.  Any hour at all...  Easy, right?","description_html":"\u003cp\u003eAll you need to do here is submit your solution a prime number of seconds after the top of the hour.  Any hour at all...  Easy, right?\u003c/p\u003e","function_template":"function y = prime_time(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('prime_time.m')\r\nassert(isempty(strfind(filetext, 'fopen')))\r\n%%\r\nx=123\r\ny = prime_time(x)\r\na=clock\r\nb=floor(polyval(a(5:6),60))\r\nif isprime(b)\r\ny_correct= y\r\nelse \r\ny_correct = NaN; \r\nend\r\nassert(isequal(y,y_correct),sprintf('%s%g%s','Time is ',datestr(now,13),', or ',b,' seconds after the hour.'))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":63,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-01-14T18:34:19.000Z","updated_at":"2025-11-22T17:34:33.000Z","published_at":"2013-01-14T18:34:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAll you need to do here is submit your solution a prime number of seconds after the top of the hour. Any hour at all... Easy, right?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":896,"title":"Sophie Germain prime","description":"In number theory, a prime number p is a *Sophie Germain prime* if 2p + 1 is also prime. For example, 23 is a Sophie Germain prime because it is a prime and 2 × 23 + 1 = 47, and 47 is also a prime number. These numbers are named after French mathematician Marie-Sophie Germain.\r\n\r\nSee \u003chttp://en.wikipedia.org/wiki/Sophie_Germain_prime Sophie Germain prime\u003e article on Wikipedia.\r\n\r\n\r\nIn this Problem , the input is a number and you must return true or false if this number is a Sophie Germain prime.","description_html":"\u003cp\u003eIn number theory, a prime number p is a \u003cb\u003eSophie Germain prime\u003c/b\u003e if 2p + 1 is also prime. For example, 23 is a Sophie Germain prime because it is a prime and 2 × 23 + 1 = 47, and 47 is also a prime number. These numbers are named after French mathematician Marie-Sophie Germain.\u003c/p\u003e\u003cp\u003eSee \u003ca href=\"http://en.wikipedia.org/wiki/Sophie_Germain_prime\"\u003eSophie Germain prime\u003c/a\u003e article on Wikipedia.\u003c/p\u003e\u003cp\u003eIn this Problem , the input is a number and you must return true or false if this number is a Sophie Germain prime.\u003c/p\u003e","function_template":"function tf = your_fcn_name(x)\r\n  tf = true;\r\nend","test_suite":"%%\r\np = 233;\r\ny_correct = true;\r\nassert(isequal(your_fcn_name(p),y_correct))\r\n\r\n%%\r\np = 23;\r\ny_correct14 = true;\r\nassert(isequal(your_fcn_name(p),y_correct14))\r\n\r\n%%\r\np = 22;\r\ny_correct14 = false;\r\nassert(isequal(your_fcn_name(p),y_correct14))\r\n\r\n%% \r\np = 1 % p must also be a prime number !!\r\ny_correct1t = false;\r\nassert(isequal(your_fcn_name(p),y_correct1t))\r\n\r\n%% \r\np = 14 % p must also be a prime number !!\r\ncorrect1t = false;\r\nassert(isequal(your_fcn_name(p),correct1t))\r\n\r\n%% \r\np = 29 \r\ncorrect1tp = true;\r\nassert(isequal(your_fcn_name(p),correct1tp))\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":2,"created_by":639,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1069,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":44,"created_at":"2012-08-10T13:04:11.000Z","updated_at":"2026-05-08T12:50:50.000Z","published_at":"2012-08-10T13:04:11.000Z","restored_at":"2018-10-10T14:57:27.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn number theory, a prime number p is a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSophie Germain prime\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e if 2p + 1 is also prime. For example, 23 is a Sophie Germain prime because it is a prime and 2 × 23 + 1 = 47, and 47 is also a prime number. These numbers are named after French mathematician Marie-Sophie Germain.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Sophie_Germain_prime\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSophie Germain prime\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e article on Wikipedia.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this Problem , the input is a number and you must return true or false if this number is a Sophie Germain prime.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2337,"title":"Sum of big primes without primes","description":"Inspired by Project Euler n°10 (I am quite obviously a fan).\r\nWith problem n°250 by Doug, you can find some global methods to compute the sum of all the primes below the input n.\r\nFor example, the sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.\r\nBut how to proceed (in time) with big number and WITHOUT the primes function ?\r\nHINTS: sum(primes(n)) is possible here but why miss the wonderfull Sieve of Eratosthenes ?\r\nhttp://en.wikipedia.org/wiki/Sieve_of_Eratosthenes","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 171px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 85.5px; transform-origin: 407px 85.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 183px 8px; transform-origin: 183px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eInspired by Project Euler n°10 (I am quite obviously a fan).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376px 8px; transform-origin: 376px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWith problem n°250 by Doug, you can find some global methods to compute the sum of all the primes below the input n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 208px 8px; transform-origin: 208px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, the sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 255.5px 8px; transform-origin: 255.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBut how to proceed (in time) with big number and WITHOUT the primes function ?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 288.5px 8px; transform-origin: 288.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHINTS: sum(primes(n)) is possible here but why miss the wonderfull Sieve of Eratosthenes ?\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ehttp://en.wikipedia.org/wiki/Sieve_of_Eratosthenes\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = big_euler10(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('big_euler10.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'primes'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 10;\r\ny_correct = 17;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 100;\r\ny_correct = 1060;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 1000;\r\ny_correct = 76127;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 10000;\r\ny_correct = 5736396;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 100000;\r\ny_correct = 454396537;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 1000000;\r\ny_correct = 37550402023;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 1000000-100;\r\ny_correct = 37542402433;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%%\r\nx = 2000000-1000;\r\ny_correct = 142781862782;\r\nassert(isequal(big_euler10(x),y_correct))\r\n%% Solution of Project Euler 10 with n=2000000\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":3,"created_by":5390,"edited_by":223089,"edited_at":"2023-06-05T10:25:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":241,"test_suite_updated_at":"2023-06-05T10:25:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-05-27T21:25:58.000Z","updated_at":"2026-04-26T18:32:38.000Z","published_at":"2014-05-27T21:51:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInspired by Project Euler n°10 (I am quite obviously a fan).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWith problem n°250 by Doug, you can find some global methods to compute the sum of all the primes below the input n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, the sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBut how to proceed (in time) with big number and WITHOUT the primes function ?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHINTS: sum(primes(n)) is possible here but why miss the wonderfull Sieve of Eratosthenes ?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://en.wikipedia.org/wiki/Sieve_of_Eratosthenes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44403,"title":"Goldbach's marginal conjecture - Write integer as sum of three primes","description":"Goldbach's strong conjecture states that every even integer greater than 2 can be expressed as the sum of two primes. For example: 4 = 2+2, 6 = 3+3, 8 = 3+5, 10 = 3+7 = 5+5, 12 = 5+7 etc.\r\n\r\nAs a corrollary, Goldbach's weak conjecture states that every odd integer greater than 7 can be expressed as the sum of three odd primes. For example: 9 = 3+3+3, 11 = 3+3+5, 13 = 3+3+7 = 3+5+5, 15 = 3+5+7 = 5+5+5 etc.\r\n\r\nA third conjecture was written by Goldbach in the margin of a letter, and (in its modern version) states that \r\n\r\n\" _Every integer greater than 5 can be expressed as the sum of three primes._ \"\r\n\r\nExamples:\r\n\r\n*  6 = 2 + 2 + 2\r\n*  7 = 2 + 2 + 3\r\n*  8 = 2 + 3 + 3 \r\n*  9 = 2 + 2 + 5 = 3 + 3 + 3 \r\n* 10 = 2 + 3 + 5\r\n* 11 = 2 + 2 + 7 = 3 + 3 + 5\r\n* 12 = 2 + 3 + 7 = 2 + 5 + 5\r\n* 13 = 3 + 3 + 7 = 3 + 5 + 5\r\n* 14 = 2 + 5 + 7\r\n* 15 = 2 + 2 + 11 = 3 + 5 + 7 = 5 + 5 + 5\r\n\r\nYour task is to write a function which takes a positive integer _n_ as input, and which returns a 1-by-3 vector _y_, which contains three numbers that are primes and whose sum equals _n_. If there exist multiple solutions for _y_, then any one of those solutions will suffice. However, _y_ must be in sorted order. You can assume that _n_ will be an integer greater than 5.\r\n\r\n","description_html":"\u003cp\u003eGoldbach's strong conjecture states that every even integer greater than 2 can be expressed as the sum of two primes. For example: 4 = 2+2, 6 = 3+3, 8 = 3+5, 10 = 3+7 = 5+5, 12 = 5+7 etc.\u003c/p\u003e\u003cp\u003eAs a corrollary, Goldbach's weak conjecture states that every odd integer greater than 7 can be expressed as the sum of three odd primes. For example: 9 = 3+3+3, 11 = 3+3+5, 13 = 3+3+7 = 3+5+5, 15 = 3+5+7 = 5+5+5 etc.\u003c/p\u003e\u003cp\u003eA third conjecture was written by Goldbach in the margin of a letter, and (in its modern version) states that\u003c/p\u003e\u003cp\u003e\" \u003ci\u003eEvery integer greater than 5 can be expressed as the sum of three primes.\u003c/i\u003e \"\u003c/p\u003e\u003cp\u003eExamples:\u003c/p\u003e\u003cul\u003e\u003cli\u003e6 = 2 + 2 + 2\u003c/li\u003e\u003cli\u003e7 = 2 + 2 + 3\u003c/li\u003e\u003cli\u003e8 = 2 + 3 + 3\u003c/li\u003e\u003cli\u003e9 = 2 + 2 + 5 = 3 + 3 + 3\u003c/li\u003e\u003cli\u003e10 = 2 + 3 + 5\u003c/li\u003e\u003cli\u003e11 = 2 + 2 + 7 = 3 + 3 + 5\u003c/li\u003e\u003cli\u003e12 = 2 + 3 + 7 = 2 + 5 + 5\u003c/li\u003e\u003cli\u003e13 = 3 + 3 + 7 = 3 + 5 + 5\u003c/li\u003e\u003cli\u003e14 = 2 + 5 + 7\u003c/li\u003e\u003cli\u003e15 = 2 + 2 + 11 = 3 + 5 + 7 = 5 + 5 + 5\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eYour task is to write a function which takes a positive integer \u003ci\u003en\u003c/i\u003e as input, and which returns a 1-by-3 vector \u003ci\u003ey\u003c/i\u003e, which contains three numbers that are primes and whose sum equals \u003ci\u003en\u003c/i\u003e. If there exist multiple solutions for \u003ci\u003ey\u003c/i\u003e, then any one of those solutions will suffice. However, \u003ci\u003ey\u003c/i\u003e must be in sorted order. You can assume that \u003ci\u003en\u003c/i\u003e will be an integer greater than 5.\u003c/p\u003e","function_template":"function y = goldbach3(n)\r\n  y = [n,n,n];\r\nend","test_suite":"%%\r\nn = 6;\r\ny = goldbach3(n);\r\ny_correct = [2,2,2];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 7;\r\ny = goldbach3(n);\r\ny_correct = [2,2,3];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 8;\r\ny = goldbach3(n);\r\ny_correct = [2,3,3];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 9;\r\ny = goldbach3(n);\r\ny_correct1 = [2,2,5];\r\ny_correct2 = [3,3,3];\r\nassert(isequal(y,y_correct1)|isequal(y,y_correct2))\r\n\r\n%%\r\nn = 10;\r\ny = goldbach3(n);\r\ny_correct = [2,3,5];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 11;\r\ny = goldbach3(n);\r\ny_correct1 = [2,2,7];\r\ny_correct2 = [3,3,5];\r\nassert(isequal(y,y_correct1)|isequal(y,y_correct2))\r\n\r\n%%\r\nn = 12;\r\ny = goldbach3(n);\r\ny_correct1 = [2,3,7];\r\ny_correct2 = [2,5,5];\r\nassert(isequal(y,y_correct1)|isequal(y,y_correct2))\r\n\r\n%%\r\nn = 13;\r\ny = goldbach3(n);\r\ny_correct1 = [3,3,7];\r\ny_correct2 = [3,5,5];\r\nassert(isequal(y,y_correct1)|isequal(y,y_correct2))\r\n\r\n%%\r\nn = 14;\r\ny = goldbach3(n);\r\ny_correct = [2,5,7];\r\nassert(isequal(y,y_correct))\r\n\r\n%%\r\nn = 15;\r\ny = goldbach3(n);\r\ny_correct1 = [2,2,11];\r\ny_correct2 = [3,5,7];\r\ny_correct3 = [5,5,5];\r\nassert(isequal(y,y_correct1)|isequal(y,y_correct2)|isequal(y,y_correct3))\r\n\r\n%%\r\nn = 101;\r\ny = goldbach3(n);\r\nassert(isequal(y,sort(y)))\r\nassert(all(isprime(y)))\r\nassert(sum(y)==n)\r\n\r\n%%\r\nn = 102;\r\ny = goldbach3(n);\r\nassert(isequal(y,sort(y)))\r\nassert(all(isprime(y)))\r\nassert(sum(y)==n)\r\n\r\n%% \r\nfor n = 250:300\r\n    y = goldbach3(n);\r\n    assert(isequal(y,sort(y)));\r\n    assert(all(isprime(y)));\r\n    assert(sum(y)==n);\r\nend\r\n\r\n%%\r\nn = randi(2000)+5; % generate a random integer greater than 5 and smaller than 2006\r\ny = goldbach3(n);\r\nassert(isequal(y,sort(y)))\r\nassert(all(isprime(y)))\r\nassert(sum(y)==n)\r\n\r\n%% \r\nvalid = zeros(1,50);\r\nfor k = 1:50\r\n    n = randi(1000)+5; % generate a random integer greater than 5 and smaller than 1006\r\n    yk = goldbach3(n);\r\n    valid(k) = (isequal(yk,sort(yk)) \u0026 all(isprime(yk)) \u0026 sum(yk)==n);\r\nend\r\nassert(all(valid));\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":2,"created_by":108199,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":76,"test_suite_updated_at":"2017-11-18T23:12:48.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2017-11-14T00:05:38.000Z","updated_at":"2026-04-15T01:39:36.000Z","published_at":"2017-11-14T01:21:48.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGoldbach's strong conjecture states that every even integer greater than 2 can be expressed as the sum of two primes. For example: 4 = 2+2, 6 = 3+3, 8 = 3+5, 10 = 3+7 = 5+5, 12 = 5+7 etc.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs a corrollary, Goldbach's weak conjecture states that every odd integer greater than 7 can be expressed as the sum of three odd primes. For example: 9 = 3+3+3, 11 = 3+3+5, 13 = 3+3+7 = 3+5+5, 15 = 3+5+7 = 5+5+5 etc.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA third conjecture was written by Goldbach in the margin of a letter, and (in its modern version) states that\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEvery integer greater than 5 can be expressed as the sum of three primes.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e6 = 2 + 2 + 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e7 = 2 + 2 + 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e8 = 2 + 3 + 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e9 = 2 + 2 + 5 = 3 + 3 + 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e10 = 2 + 3 + 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e11 = 2 + 2 + 7 = 3 + 3 + 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e12 = 2 + 3 + 7 = 2 + 5 + 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e13 = 3 + 3 + 7 = 3 + 5 + 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e14 = 2 + 5 + 7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e15 = 2 + 2 + 11 = 3 + 5 + 7 = 5 + 5 + 5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour task is to write a function which takes a positive integer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e as input, and which returns a 1-by-3 vector\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which contains three numbers that are primes and whose sum equals\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. If there exist multiple solutions for\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, then any one of those solutions will suffice. However,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e must be in sorted order. You can assume that\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will be an integer greater than 5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2910,"title":"Mersenne Primes vs. All Primes","description":"A Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number. \u003chttps://www.mathworks.com/matlabcentral/cody/problems/525-mersenne-primes Problem 525\u003e asks the user to determine if a number is a Mersenne prime. In this problem, you are tasked with returning the number of primes numbers below the input number, n, that are Mersenne primes and the fraction of all primes below that input number that the Mersenne primes represent.\r\n\r\nFor example, for n = 100, there are 25 primes numbers: 2, 3, 5, 7, ..., 89, 97. As far as Mersenne primes go, there are only three that are less than 100: 2^2 - 1 = 3, 2^3 - 1 = 7, and 2^5 - 1 = 31. The corresponding fraction would be 3/25.","description_html":"\u003cp\u003eA Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number. \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/525-mersenne-primes\"\u003eProblem 525\u003c/a\u003e asks the user to determine if a number is a Mersenne prime. In this problem, you are tasked with returning the number of primes numbers below the input number, n, that are Mersenne primes and the fraction of all primes below that input number that the Mersenne primes represent.\u003c/p\u003e\u003cp\u003eFor example, for n = 100, there are 25 primes numbers: 2, 3, 5, 7, ..., 89, 97. As far as Mersenne primes go, there are only three that are less than 100: 2^2 - 1 = 3, 2^3 - 1 = 7, and 2^5 - 1 = 31. The corresponding fraction would be 3/25.\u003c/p\u003e","function_template":"function [y,f] = Mersenne_prime_comp(n)\r\n y = 1;\r\n f = 0;\r\nend","test_suite":"%%\r\nn = 1e2;\r\ny_correct = 3;\r\nf_correct = 3/25;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(isequal(f,f_correct))\r\n\r\n%%\r\nn = 1e3;\r\ny_correct = 4;\r\nf_correct = 0.023809523809524;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n\r\n%%\r\nn = 1e4;\r\ny_correct = 5;\r\nf_correct = 0.004068348250610;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n\r\n%%\r\nn = 1e5;\r\ny_correct = 5;\r\nf_correct = 5.212677231025855e-04;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n\r\n%%\r\nn = 1e6;\r\ny_correct = 7;\r\nf_correct = 8.917424647761727e-05;\r\n[y,f] = Mersenne_prime_comp(n);\r\nassert(isequal(y,y_correct))\r\nassert(abs(f-f_correct)\u003c(10*eps))\r\n","published":true,"deleted":false,"likes_count":8,"comments_count":2,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":849,"test_suite_updated_at":"2015-02-01T04:14:08.000Z","rescore_all_solutions":false,"group_id":29,"created_at":"2015-02-01T03:56:07.000Z","updated_at":"2026-05-06T01:12:18.000Z","published_at":"2015-02-01T04:14:08.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA Mersenne prime (M) is a prime number of the form M = 2^p - 1, where p is another prime number.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/525-mersenne-primes\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 525\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asks the user to determine if a number is a Mersenne prime. In this problem, you are tasked with returning the number of primes numbers below the input number, n, that are Mersenne primes and the fraction of all primes below that input number that the Mersenne primes represent.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, for n = 100, there are 25 primes numbers: 2, 3, 5, 7, ..., 89, 97. As far as Mersenne primes go, there are only three that are less than 100: 2^2 - 1 = 3, 2^3 - 1 = 7, and 2^5 - 1 = 31. The corresponding fraction would be 3/25.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2595,"title":"Polite numbers. Politeness.","description":"A polite number is an integer that sums of two or more consecutive positive integers.\r\nPoliteness of a positive integer is a number of nontrivial ways to write n as a sum of two or more consecutive positive integers.\r\n\r\nFor example _9 = 4+5 = 2+3+4_  and politeness of 9 is 2.\r\n\r\nGiven _N_ return politeness of _N_.\r\n\r\nSee also \u003chttp://www.mathworks.co.uk/matlabcentral/cody/problems/2593 2593\u003e","description_html":"\u003cp\u003eA polite number is an integer that sums of two or more consecutive positive integers.\r\nPoliteness of a positive integer is a number of nontrivial ways to write n as a sum of two or more consecutive positive integers.\u003c/p\u003e\u003cp\u003eFor example \u003ci\u003e9 = 4+5 = 2+3+4\u003c/i\u003e  and politeness of 9 is 2.\u003c/p\u003e\u003cp\u003eGiven \u003ci\u003eN\u003c/i\u003e return politeness of \u003ci\u003eN\u003c/i\u003e.\u003c/p\u003e\u003cp\u003eSee also \u003ca href = \"http://www.mathworks.co.uk/matlabcentral/cody/problems/2593\"\u003e2593\u003c/a\u003e\u003c/p\u003e","function_template":"function P = politeness(N)\r\n  P=N;\r\nend","test_suite":"%%\r\nx = 1;\r\ny_correct = 0;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 2;\r\ny_correct = 0;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 3;\r\ny_correct = 1;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 7;\r\ny_correct = 1;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 9;\r\ny_correct = 2;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 15;\r\ny_correct = 3;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 18;\r\ny_correct = 2;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 21;\r\ny_correct = 3;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 1024;\r\ny_correct = 0;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 1025;\r\ny_correct = 5;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 25215;\r\ny_correct = 11;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 62;\r\ny_correct = 1;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 63;\r\ny_correct = 5;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nx = 65;\r\ny_correct = 3;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\n% anti-lookup \u0026 clue\r\nnums=primes(200);\r\npattern=[1 nums([false ~randi([0 25],1,45)])];\r\nx=prod(pattern)*2^randi([0 5]);\r\ny_correct=2^numel(pattern)/2-1;\r\nassert(isequal(politeness(x),y_correct))\r\n%%\r\nfor k=randi(2e4,1,20)\r\n  assert(isequal(politeness(k*(k-1))+1,(politeness(k)+1)*(politeness(k-1)+1)))\r\nend","published":true,"deleted":false,"likes_count":8,"comments_count":6,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":189,"test_suite_updated_at":"2014-09-17T15:38:21.000Z","rescore_all_solutions":false,"group_id":8,"created_at":"2014-09-16T22:47:12.000Z","updated_at":"2026-05-05T05:28:08.000Z","published_at":"2014-09-17T10:56:54.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA polite number is an integer that sums of two or more consecutive positive integers. Politeness of a positive integer is a number of nontrivial ways to write n as a sum of two or more consecutive positive integers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e9 = 4+5 = 2+3+4\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and politeness of 9 is 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e return politeness of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee also\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.co.uk/matlabcentral/cody/problems/2593\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e2593\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1672,"title":"Leftovers?  Again?!","description":"I am thinking of a positive number X.  To determine what number I am thinking of, I will give you two 1xN vectors.  The first vector (V1) is several numbers, none of which will share a factor.  The second vector (V2) is the remainder of X when divided by each of the numbers in V1. Calculate what the lowest possible value of X can be given these criteria.  For example:\r\n\r\nV1 = [2 3] ; V2 = [1 2]\r\n\r\nwould give an X value of 5.  There are an infinite number of other values of X that would satisfy V1 and V2, but I want the lowest one.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; transform-origin: 332px 82.5px; vertical-align: baseline; perspective-origin: 332px 82.5px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 42px; white-space: pre-wrap; perspective-origin: 309px 42px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eI am thinking of a positive number X. To determine what number I am thinking of, I will give you two 1xN vectors. The first vector (V1) is several numbers, none of which will share a factor. The second vector (V2) is the remainder of X when divided by each of the numbers in V1. Calculate what the lowest possible value of X can be given these criteria. For example:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 10.5px; white-space: pre-wrap; perspective-origin: 309px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eV1 = [2 3] ; V2 = [1 2]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; transform-origin: 309px 21px; white-space: pre-wrap; perspective-origin: 309px 21px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; transform-origin: 0px 0px; perspective-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ewould give an X value of 5. There are an infinite number of other values of X that would satisfy V1 and V2, but I want the lowest one.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function X = leftovers(n,a)\r\n X = pi;\r\nend","test_suite":"%!cp leftovers.m safe\r\n%!rm *.*\r\n%!mv safe leftovers.m\r\n%!rm @*\r\n\r\n% Clean user's function from some known jailbreaking mechanisms\r\nfid = fopen('leftovers.m');\r\nst = regexprep(char(fread(fid)'), '!', 'error(''No shell commands!''); %');\r\nst = regexprep(st, 'feval', 'error(''No fancy functions!''); %');\r\nst = regexprep(st, 'str2func', 'error(''No fancy functions!''); %');\r\nst = regexprep(st, 'regex', 'error(''No fancy functions!''); %');\r\nst = regexprep(st, 'system', 'error(''No shell commands!''); %');\r\nst = regexprep(st, 'dos', 'error(''No shell commands!''); %');\r\nst = regexprep(st, 'unix', 'error(''No shell commands!''); %');\r\nst = regexprep(st, 'perl', 'error(''No external languages commands!''); %');\r\nst = regexprep(st, 'java', 'error(''No external languages commands!''); %');\r\nst = regexprep(st, 'assert', 'error(''No overwriting!''); %');\r\nfclose(fid)\r\n\r\nfid = fopen('leftovers.m' , 'w');\r\nfwrite(fid,st);\r\nfclose(fid)\r\n%%\r\nV1 = [2 3] ; V2 = [1 2];; y_correct = 5; assert(isequal(leftovers(V1,V2),y_correct))\r\n%%\r\nV1=[3 5 7] ; V2=[1 2 3]; y_correct = 52; assert(isequal(leftovers(V1,V2),y_correct))\r\n%%\r\nV1=[3 4 5] ; V2=[2 3 1]; y_correct = 11; assert(isequal(leftovers(V1,V2),y_correct))\r\n%%\r\nV1=[4 9 25] ; V2=[3 2 7]; y_correct = 407; assert(isequal(leftovers(V1,V2),y_correct))\r\n%%\r\nV1=[9 10 77] ; V2=[1 2 69]; y_correct = 6922; assert(isequal(leftovers(V1,V2),y_correct))\r\n%%\r\na=primes(30);\r\nb=ceil(8*rand()+2)\r\nV1=a(1:b);V2=1:b;\r\ny_correct=[23 53 1523 29243 299513 4383593 188677703 5765999453];\r\nassert(isequal(leftovers(V1,V2),y_correct(b-2)))\r\n%%\r\nV1=[leftovers([6 35],[3 9]) leftovers([3 5 7],[1 3 1])];\r\nassert(isequal(leftovers(V1,V1-8),379))\r\n%%\r\n% Discourage the for x=1:inf loops\r\nV1=[74 93 145 161 209 221]; V2=[66 85 137 153 201 213];\r\ny_correct=7420738134802;\r\nassert(isequal(leftovers(V1,V2),y_correct))\r\n%%\r\n% Discourage the for x=1:inf loops\r\nV1=[17 82 111 155 203 247 253] ; V2=[11 50 68 95 124 150 154];\r\ny_correct=59652745309190;\r\nassert(isequal(leftovers(V1,V2),y_correct))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":10,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":32,"test_suite_updated_at":"2020-09-29T13:24:49.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-06-21T18:45:36.000Z","updated_at":"2025-11-22T17:35:45.000Z","published_at":"2013-06-21T18:45:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI am thinking of a positive number X. To determine what number I am thinking of, I will give you two 1xN vectors. The first vector (V1) is several numbers, none of which will share a factor. The second vector (V2) is the remainder of X when divided by each of the numbers in V1. Calculate what the lowest possible value of X can be given these criteria. For example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eV1 = [2 3] ; V2 = [1 2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewould give an X value of 5. There are an infinite number of other values of X that would satisfy V1 and V2, but I want the lowest one.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":60,"title":"The Goldbach Conjecture","description":"The Goldbach conjecture asserts that every even integer greater than 2 can be expressed as the sum of two primes.\r\nGiven the even integer n, return primes p1 and p2 that satisfy the condition n = p1 + p2. Note that the primes are not always unique. The test is not sensitive to order or uniqueness. You just need to meet the appropriate conditions.\r\nExample:\r\n Input  n = 286\r\n Output (any of the following is acceptable) \r\n        [  3 283]\r\n        [283   3]\r\n        [  5 281]\r\n        [107 179]\r\n        [137 149]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 255.033px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 127.517px; transform-origin: 407px 127.517px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.5px 8px; transform-origin: 12.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eGoldbach conjecture\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 287px 8px; transform-origin: 287px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e asserts that every even integer greater than 2 can be expressed as the sum of two primes.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.5px 8px; transform-origin: 368.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the even integer n, return primes p1 and p2 that satisfy the condition n = p1 + p2. Note that the primes are not always unique. The test is not sensitive to order or uniqueness. You just need to meet the appropriate conditions.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.5px 8px; transform-origin: 28.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 143.033px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 71.5167px; transform-origin: 404px 71.5167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 60px 8.5px; tab-size: 4; transform-origin: 60px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003e Input  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 28px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 28px 8.5px; \"\u003en = 286\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 180px 8.5px; tab-size: 4; transform-origin: 180px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e Output (any of the following is acceptable) \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        [  3 283]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        [283   3]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        [  5 281]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        [107 179]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 68px 8.5px; tab-size: 4; transform-origin: 68px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        [137 149]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [p1,p2] = goldbach(n)\r\n  p1 = n;\r\n  p2 = n;\r\nend","test_suite":"%%\r\nfiletext = fileread('goldbach.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)\r\n\r\n%%\r\nnList = 28:6:76;\r\nfor i = 1:length(nList)\r\n  n = nList(i);\r\n  [p1,p2] = goldbach(n)\r\n  assert(isprime(p1) \u0026\u0026 isprime(p2) \u0026\u0026 (p1+p2==n));\r\nend\r\n\r\n%%\r\nnList = [18 20 22 100 102 114 1000 2000 36 3600];\r\nfor i = 1:length(nList)\r\n  n = nList(i);\r\n  [p1,p2] = goldbach(n)\r\n  assert(isprime(p1) \u0026\u0026 isprime(p2) \u0026\u0026 (p1+p2==n));\r\nend","published":true,"deleted":false,"likes_count":60,"comments_count":17,"created_by":1,"edited_by":223089,"edited_at":"2023-06-05T15:48:22.000Z","deleted_by":null,"deleted_at":null,"solvers_count":5982,"test_suite_updated_at":"2023-06-05T15:48:22.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:25.000Z","updated_at":"2026-05-08T20:48:29.000Z","published_at":"2012-01-18T01:00:25.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGoldbach conjecture\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asserts that every even integer greater than 2 can be expressed as the sum of two primes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the even integer n, return primes p1 and p2 that satisfy the condition n = p1 + p2. Note that the primes are not always unique. The test is not sensitive to order or uniqueness. You just need to meet the appropriate conditions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input  n = 286\\n Output (any of the following is acceptable) \\n        [  3 283]\\n        [283   3]\\n        [  5 281]\\n        [107 179]\\n        [137 149]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":64,"title":"The Goldbach Conjecture, Part 2","description":"The \u003chttp://en.wikipedia.org/wiki/Goldbach's_conjecture Goldbach\nconjecture\u003e asserts that every even integer greater than 2 can be\nexpressed as the sum of two primes.\n \nGiven the even integer n, return c, the number of different ways two primes can be added to result in n. Only count a pair once; the order is unimportant.\n\nExample:\n\n Input  n = 10\n Output c is 2\n\nbecause of the prime pairs [3 7] and [5 5].\n\n Input  n = 50\n Output c is 4\n\nbecause of [3 47], [7 43], [13 37], and [19 31].\n","description_html":"\u003cp\u003eThe \u003ca href=\"http://en.wikipedia.org/wiki/Goldbach's_conjecture\"\u003eGoldbach\nconjecture\u003c/a\u003e asserts that every even integer greater than 2 can be\nexpressed as the sum of two primes.\u003c/p\u003e\u003cp\u003eGiven the even integer n, return c, the number of different ways two primes can be added to result in n. Only count a pair once; the order is unimportant.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e Input  n = 10\n Output c is 2\u003c/pre\u003e\u003cp\u003ebecause of the prime pairs [3 7] and [5 5].\u003c/p\u003e\u003cpre\u003e Input  n = 50\n Output c is 4\u003c/pre\u003e\u003cp\u003ebecause of [3 47], [7 43], [13 37], and [19 31].\u003c/p\u003e","function_template":"function c = goldbach2(n)\n  c = 1;\nend","test_suite":"%%\nn = 6;\nc_correct = 1;\nassert(isequal(goldbach2(n),c_correct))\n\n%%\nn = 10;\nc_correct = 2;\nassert(isequal(goldbach2(n),c_correct))\n\n%%\nn = 50;\nc_correct = 4;\nassert(isequal(goldbach2(n),c_correct))\n\n%%\nn = 480;\nc_correct = 29;\nassert(isequal(goldbach2(n),c_correct))","published":true,"deleted":false,"likes_count":18,"comments_count":4,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2417,"test_suite_updated_at":"2012-01-18T01:00:26.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:26.000Z","updated_at":"2026-05-05T20:42:32.000Z","published_at":"2012-01-18T01:00:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Goldbach's_conjecture\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eGoldbach conjecture\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e asserts that every even integer greater than 2 can be expressed as the sum of two primes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the even integer n, return c, the number of different ways two primes can be added to result in n. Only count a pair once; the order is unimportant.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input  n = 10\\n Output c is 2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ebecause of the prime pairs [3 7] and [5 5].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input  n = 50\\n Output c is 4]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ebecause of [3 47], [7 43], [13 37], and [19 31].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":83,"title":"Prime factor digits","description":"Consider the following number system. Calculate the prime factorization for each number n, then represent the prime factors in a vector like so:\r\n       13 11 7 5 3 2\r\n      ---------------\r\n    2:             1\r\n    3:           1 0\r\n    4:             2\r\n    5:         1 0 0\r\n    6:           1 1\r\n   12:           1 2\r\n   14:       1 0 0 1\r\n   18:           2 1\r\n   26:   1 0 0 0 0 1\r\n   60:         1 1 2\r\nEach \"place\" in the number system represents a prime number. Given n, return the vector p.\r\nAs shown above, if n = 26, then p = [1 0 0 0 0 1].\r\nThe input n is always an integer greater than 1. Suppress any leading zeros. The length of the vector is determined by the largest prime factor.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 409.2px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 204.6px; transform-origin: 407px 204.6px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.5px 8px; transform-origin: 368.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eConsider the following number system. Calculate the prime factorization for each number n, then represent the prime factors in a vector like so:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 245.2px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 122.6px; transform-origin: 404px 122.6px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e       13 11 7 5 3 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 84px 8.5px; transform-origin: 84px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e      ---------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    2:             1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    3:           1 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    4:             2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    5:         1 0 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e    6:           1 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   12:           1 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   14:       1 0 0 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   18:           2 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   26:   1 0 0 0 0 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e   60:         1 1 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 289.5px 8px; transform-origin: 289.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eEach \"place\" in the number system represents a prime number. Given n, return the vector p.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 153px 8px; transform-origin: 153px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs shown above, if n = 26, then p = [1 0 0 0 0 1].\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe input n is always an integer greater than 1. Suppress any leading zeros. The length of the vector is determined by the largest prime factor.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function p = factor_digits(n)\r\n  p = 0;\r\nend","test_suite":"%%\r\nn = 26;\r\np_correct = [1 0 0 0 0 1];\r\nassert(isequal(factor_digits(n),p_correct))\r\n\r\n%%\r\nn = 168;\r\np_correct = [1 0 1 3];\r\nassert(isequal(factor_digits(n),p_correct))\r\n\r\n%%\r\nn = 2;\r\np_correct = 1;\r\nassert(isequal(factor_digits(n),p_correct))\r\n\r\n%%\r\nn = 1444;\r\np_correct = 2*[1 0 0 0 0 0 0 1];\r\nassert(isequal(factor_digits(n),p_correct))\r\n\r\n%%\r\nn = 47;\r\np_correct = [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0];\r\nassert(isequal(factor_digits(n),p_correct))\r\n\r\n%%\r\nn = 999;\r\np_correct = [1 0 0 0 0 0 0 0 0 0 3 0];\r\nassert(isequal(factor_digits(n),p_correct))\r\n\r\n%%\r\nn = 20;\r\np_correct = [1 0 2];\r\nassert(isequal(factor_digits(n),p_correct))","published":true,"deleted":false,"likes_count":28,"comments_count":6,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2543,"test_suite_updated_at":"2021-08-08T11:30:25.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:29.000Z","updated_at":"2026-05-05T20:56:35.000Z","published_at":"2012-01-18T01:00:29.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the following number system. Calculate the prime factorization for each number n, then represent the prime factors in a vector like so:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[       13 11 7 5 3 2\\n      ---------------\\n    2:             1\\n    3:           1 0\\n    4:             2\\n    5:         1 0 0\\n    6:           1 1\\n   12:           1 2\\n   14:       1 0 0 1\\n   18:           2 1\\n   26:   1 0 0 0 0 1\\n   60:         1 1 2]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach \\\"place\\\" in the number system represents a prime number. Given n, return the vector p.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs shown above, if n = 26, then p = [1 0 0 0 0 1].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe input n is always an integer greater than 1. Suppress any leading zeros. The length of the vector is determined by the largest prime factor.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":1095,"title":"Circular Primes (based on Project Euler, problem 35)","description":"The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.\r\n\r\nThere are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.\r\n\r\nGiven a number x, write a MATLAB script that will tell you the number of circular primes less than or equal to x as well as a sorted list of what the circular prime numbers are.","description_html":"\u003cp\u003eThe number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.\u003c/p\u003e\u003cp\u003eThere are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.\u003c/p\u003e\u003cp\u003eGiven a number x, write a MATLAB script that will tell you the number of circular primes less than or equal to x as well as a sorted list of what the circular prime numbers are.\u003c/p\u003e","function_template":"function [how_many what_numbers]=circular_prime(x)\r\n    how_many=3;\r\n    what_numbers=[2 3 5];\r\nend","test_suite":"%%\r\n[y numbers]=circular_prime(197)\r\nassert(isequal(y,16)\u0026\u0026isequal(numbers,[2 3 5 7 11 13 17 31 37 71 73 79 97 113 131 197]))\r\n%%\r\n[y numbers]=circular_prime(100)\r\nassert(isequal(y,13)\u0026\u0026isequal(numbers,[2 3 5 7 11 13 17 31 37 71 73 79 97]))\r\n%%\r\n[y numbers]=circular_prime(250)\r\nassert(isequal(y,17)\u0026\u0026isequal(numbers,[2 3 5 7 11 13 17 31 37 71 73 79 97 113 131 197 199]))\r\n%%\r\n[y numbers]=circular_prime(2000)\r\nassert(isequal(y,27)\u0026\u0026isequal(numbers,[2 3 5 7 11 13 17 31 37 71 73 79 97 113 131 197 199 311 337 373 719 733 919 971 991 1193 1931]))\r\n%%\r\n[y numbers]=circular_prime(10000)\r\nassert(isequal(y,33)\u0026\u0026isequal(numbers,[2 3 5 7 11 13 17 31 37 71 73 79 97 113 131 197 199 311 337 373 719 733 919 971 991 1193 1931 3119 3779 7793 7937 9311 9377]))\r\n%%\r\n[y numbers]=circular_prime(54321)\r\nassert(isequal(y,38)\u0026\u0026isequal(numbers,[2 3 5 7 11 13 17 31 37 71 73 79 97 113 131 197 199 311 337 373 719 733 919 971 991 1193 1931 3119 3779 7793 7937 9311 9377 11939 19391 19937 37199 39119]))\r\n","published":true,"deleted":false,"likes_count":10,"comments_count":6,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":655,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-12-05T18:02:09.000Z","updated_at":"2026-05-06T03:26:47.000Z","published_at":"2012-12-05T18:02:09.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a number x, write a MATLAB script that will tell you the number of circular primes 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