{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","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":"2025-12-14T00:00:00.000Z","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":1761,"title":"Primes Faster for Large N","description":"This Challenge is to improve the \"primes\" function for speed. This may be accomplished by fixing memory usage.\r\n\r\nThe Matlab function \"primes\" has a very efficient sieving method but it suffers from a memory usage issue that may bump into a user's RAM size causing \"out of memory\", significant slow down, or Matlab freeze.\r\n\r\nCody appears to have 2GB of RAM based upon \"out of memory\" messages observed.\r\n\r\nThe test case of 2^28 starts to bump into memory limit affects but will complete with the standard primes function.\r\n\r\nThe reference solution can process N=2^33 on a 16GB machine in 284sec.\r\n\r\n*Input:* N  (max of primes to find)\r\n\r\n*Output:* vector of primes  (all primes less than or equal to N)\r\n\r\n*Scoring:* Time to find all primes \u003c 2^28\r\n\r\n*Hints:*\r\n\r\n  1) Doubles use 8 bytes; logicals use 1 byte\r\n  2) The method p = p(p\u003e0); is good but can be improved\r\n  3) The method p = 1:2:n; creates a double and is a little slow\r\n  4) Usage of profiler and Task Manager combined give performance insights\r\n\r\n*Related:* \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1763-primes-for-large-n-2-30-system-memory-limit Primes 2^30\u003e\r\n\r\n*Matlab 2014a incorporated the speed enhancement of logicals*","description_html":"\u003cp\u003eThis Challenge is to improve the \"primes\" function for speed. This may be accomplished by fixing memory usage.\u003c/p\u003e\u003cp\u003eThe Matlab function \"primes\" has a very efficient sieving method but it suffers from a memory usage issue that may bump into a user's RAM size causing \"out of memory\", significant slow down, or Matlab freeze.\u003c/p\u003e\u003cp\u003eCody appears to have 2GB of RAM based upon \"out of memory\" messages observed.\u003c/p\u003e\u003cp\u003eThe test case of 2^28 starts to bump into memory limit affects but will complete with the standard primes function.\u003c/p\u003e\u003cp\u003eThe reference solution can process N=2^33 on a 16GB machine in 284sec.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e N  (max of primes to find)\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e vector of primes  (all primes less than or equal to N)\u003c/p\u003e\u003cp\u003e\u003cb\u003eScoring:\u003c/b\u003e Time to find all primes \u0026lt; 2^28\u003c/p\u003e\u003cp\u003e\u003cb\u003eHints:\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e1) Doubles use 8 bytes; logicals use 1 byte\r\n2) The method p = p(p\u0026gt;0); is good but can be improved\r\n3) The method p = 1:2:n; creates a double and is a little slow\r\n4) Usage of profiler and Task Manager combined give performance insights\r\n\u003c/pre\u003e\u003cp\u003e\u003cb\u003eRelated:\u003c/b\u003e \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1763-primes-for-large-n-2-30-system-memory-limit\"\u003ePrimes 2^30\u003c/a\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eMatlab 2014a incorporated the speed enhancement of logicals\u003c/b\u003e\u003c/p\u003e","function_template":"function p = primes_faster(n) % The mathworks primes function\r\n%PRIMES Generate list of prime numbers.\r\n%   PRIMES(N) is a row vector of the prime numbers less than or \r\n%   equal to N.  A prime number is one that has no factors other\r\n%   than 1 and itself.\r\n%\r\n%   Class support for input N:\r\n%      float: double, single\r\n%\r\n%   See also FACTOR, ISPRIME.\r\n\r\n%   Copyright 1984-2004 The MathWorks, Inc. \r\n%   $Revision: 1.16.4.3 $  $Date: 2010/08/23 23:13:13 $\r\n\r\nif length(n)~=1 \r\n  error(message('MATLAB:primes:InputNotScalar')); \r\nend\r\nif n \u003c 2, p = zeros(1,0,class(n)); return, end\r\np = 1:2:n;\r\nq = length(p);\r\np(1) = 2;\r\nfor k = 3:2:sqrt(n)\r\n  if p((k+1)/2)\r\n     p(((k*k+1)/2):k:q) = 0;\r\n  end\r\nend\r\np = p(p\u003e0);\r\n\r\nend","test_suite":"feval(@assignin,'caller','score',30); %\r\n%%\r\ntic\r\nassert(isequal(primes_faster(1),primes(1)))\r\nassert(isequal(primes_faster(2),primes(2)))\r\nfor i=1:100\r\n n=randi(2000,1);\r\n assert(isequal(primes_faster(n),primes(n)))\r\nend\r\ntoc\r\n%%\r\ntic\r\nta=clock;\r\n p = primes_faster(2^28);\r\nt1=etime(clock,ta); % time in sec\r\n\r\nfprintf('P 2^28 %12i %10.3f\\n',length(p),t1)\r\n\r\nassert(isequal(size(unique(p),2),14630843))\r\n\r\nptr=randi(7603553,1,10); % small to avoid timeout\r\n\r\npchk=double(p(ptr));\r\n\r\nassert(all(isprime(pchk)))\r\n\r\nfeval(  @assignin,'caller','score',floor(min(30,t1))  );\r\ntoc","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":56,"test_suite_updated_at":"2013-08-07T00:21:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-07-30T02:37:44.000Z","updated_at":"2025-12-15T18:33:37.000Z","published_at":"2013-07-30T04:30:58.000Z","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\u003eThis Challenge is to improve the \\\"primes\\\" function for speed. This may be accomplished by fixing memory usage.\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\u003eThe Matlab function \\\"primes\\\" has a very efficient sieving method but it suffers from a memory usage issue that may bump into a user's RAM size causing \\\"out of memory\\\", significant slow down, or Matlab freeze.\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\u003eCody appears to have 2GB of RAM based upon \\\"out of memory\\\" messages observed.\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\u003eThe test case of 2^28 starts to bump into memory limit affects but will complete with the standard 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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe reference solution can process N=2^33 on a 16GB machine in 284sec.\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\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e N (max of primes to find)\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\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e vector of primes (all primes less than or equal to 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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Time to find all primes \u0026lt; 2^28\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\u003eHints:\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[1) Doubles use 8 bytes; logicals use 1 byte\\n2) The method p = p(p\u003e0); is good but can be improved\\n3) The method p = 1:2:n; creates a double and is a little slow\\n4) Usage of profiler and Task Manager combined give performance insights]]\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\u003eRelated:\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.com/matlabcentral/cody/problems/1763-primes-for-large-n-2-30-system-memory-limit\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ePrimes 2^30\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\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\u003eMatlab 2014a incorporated the speed enhancement of logicals\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":1761,"title":"Primes Faster for Large N","description":"This Challenge is to improve the \"primes\" function for speed. This may be accomplished by fixing memory usage.\r\n\r\nThe Matlab function \"primes\" has a very efficient sieving method but it suffers from a memory usage issue that may bump into a user's RAM size causing \"out of memory\", significant slow down, or Matlab freeze.\r\n\r\nCody appears to have 2GB of RAM based upon \"out of memory\" messages observed.\r\n\r\nThe test case of 2^28 starts to bump into memory limit affects but will complete with the standard primes function.\r\n\r\nThe reference solution can process N=2^33 on a 16GB machine in 284sec.\r\n\r\n*Input:* N  (max of primes to find)\r\n\r\n*Output:* vector of primes  (all primes less than or equal to N)\r\n\r\n*Scoring:* Time to find all primes \u003c 2^28\r\n\r\n*Hints:*\r\n\r\n  1) Doubles use 8 bytes; logicals use 1 byte\r\n  2) The method p = p(p\u003e0); is good but can be improved\r\n  3) The method p = 1:2:n; creates a double and is a little slow\r\n  4) Usage of profiler and Task Manager combined give performance insights\r\n\r\n*Related:* \u003chttp://www.mathworks.com/matlabcentral/cody/problems/1763-primes-for-large-n-2-30-system-memory-limit Primes 2^30\u003e\r\n\r\n*Matlab 2014a incorporated the speed enhancement of logicals*","description_html":"\u003cp\u003eThis Challenge is to improve the \"primes\" function for speed. This may be accomplished by fixing memory usage.\u003c/p\u003e\u003cp\u003eThe Matlab function \"primes\" has a very efficient sieving method but it suffers from a memory usage issue that may bump into a user's RAM size causing \"out of memory\", significant slow down, or Matlab freeze.\u003c/p\u003e\u003cp\u003eCody appears to have 2GB of RAM based upon \"out of memory\" messages observed.\u003c/p\u003e\u003cp\u003eThe test case of 2^28 starts to bump into memory limit affects but will complete with the standard primes function.\u003c/p\u003e\u003cp\u003eThe reference solution can process N=2^33 on a 16GB machine in 284sec.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e N  (max of primes to find)\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e vector of primes  (all primes less than or equal to N)\u003c/p\u003e\u003cp\u003e\u003cb\u003eScoring:\u003c/b\u003e Time to find all primes \u0026lt; 2^28\u003c/p\u003e\u003cp\u003e\u003cb\u003eHints:\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e1) Doubles use 8 bytes; logicals use 1 byte\r\n2) The method p = p(p\u0026gt;0); is good but can be improved\r\n3) The method p = 1:2:n; creates a double and is a little slow\r\n4) Usage of profiler and Task Manager combined give performance insights\r\n\u003c/pre\u003e\u003cp\u003e\u003cb\u003eRelated:\u003c/b\u003e \u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1763-primes-for-large-n-2-30-system-memory-limit\"\u003ePrimes 2^30\u003c/a\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eMatlab 2014a incorporated the speed enhancement of logicals\u003c/b\u003e\u003c/p\u003e","function_template":"function p = primes_faster(n) % The mathworks primes function\r\n%PRIMES Generate list of prime numbers.\r\n%   PRIMES(N) is a row vector of the prime numbers less than or \r\n%   equal to N.  A prime number is one that has no factors other\r\n%   than 1 and itself.\r\n%\r\n%   Class support for input N:\r\n%      float: double, single\r\n%\r\n%   See also FACTOR, ISPRIME.\r\n\r\n%   Copyright 1984-2004 The MathWorks, Inc. \r\n%   $Revision: 1.16.4.3 $  $Date: 2010/08/23 23:13:13 $\r\n\r\nif length(n)~=1 \r\n  error(message('MATLAB:primes:InputNotScalar')); \r\nend\r\nif n \u003c 2, p = zeros(1,0,class(n)); return, end\r\np = 1:2:n;\r\nq = length(p);\r\np(1) = 2;\r\nfor k = 3:2:sqrt(n)\r\n  if p((k+1)/2)\r\n     p(((k*k+1)/2):k:q) = 0;\r\n  end\r\nend\r\np = p(p\u003e0);\r\n\r\nend","test_suite":"feval(@assignin,'caller','score',30); %\r\n%%\r\ntic\r\nassert(isequal(primes_faster(1),primes(1)))\r\nassert(isequal(primes_faster(2),primes(2)))\r\nfor i=1:100\r\n n=randi(2000,1);\r\n assert(isequal(primes_faster(n),primes(n)))\r\nend\r\ntoc\r\n%%\r\ntic\r\nta=clock;\r\n p = primes_faster(2^28);\r\nt1=etime(clock,ta); % time in sec\r\n\r\nfprintf('P 2^28 %12i %10.3f\\n',length(p),t1)\r\n\r\nassert(isequal(size(unique(p),2),14630843))\r\n\r\nptr=randi(7603553,1,10); % small to avoid timeout\r\n\r\npchk=double(p(ptr));\r\n\r\nassert(all(isprime(pchk)))\r\n\r\nfeval(  @assignin,'caller','score',floor(min(30,t1))  );\r\ntoc","published":true,"deleted":false,"likes_count":1,"comments_count":1,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":56,"test_suite_updated_at":"2013-08-07T00:21:13.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2013-07-30T02:37:44.000Z","updated_at":"2025-12-15T18:33:37.000Z","published_at":"2013-07-30T04:30:58.000Z","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\u003eThis Challenge is to improve the \\\"primes\\\" function for speed. This may be accomplished by fixing memory usage.\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\u003eThe Matlab function \\\"primes\\\" has a very efficient sieving method but it suffers from a memory usage issue that may bump into a user's RAM size causing \\\"out of memory\\\", significant slow down, or Matlab freeze.\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\u003eCody appears to have 2GB of RAM based upon \\\"out of memory\\\" messages observed.\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\u003eThe test case of 2^28 starts to bump into memory limit affects but will complete with the standard 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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe reference solution can process N=2^33 on a 16GB machine in 284sec.\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\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e N (max of primes to find)\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\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e vector of primes (all primes less than or equal to N)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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