Problem 51798. Label primes with the Erdos-Selfridge classification

Created by ChrisR

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{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Erdos and Selfridge developed a scheme for classifying a prime number </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"p\"/></w:customXmlPr><w:r><w:t>p</w:t></w:r></w:customXml><w:r><w:t>: If the only factors of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"p+1\"/></w:customXmlPr><w:r><w:t>p+1</w:t></w:r></w:customXml><w:r><w:t> are 2 and 3, then put </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"p\"/></w:customXmlPr><w:r><w:t>p</w:t></w:r></w:customXml><w:r><w:t> in class 1. Otherwise, find the largest class </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>r</w:t></w:r></w:customXml><w:r><w:t> of the factors of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"p+1\"/></w:customXmlPr><w:r><w:t>p+1</w:t></w:r></w:customXml><w:r><w:t> and put </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"p\"/></w:customXmlPr><w:r><w:t>p</w:t></w:r></w:customXml><w:r><w:t> in class </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"r+1\"/></w:customXmlPr><w:r><w:t>r+1</w:t></w:r></w:customXml><w:r><w:t>. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For example, 11 is in class 1 because 12 has prime factors 2, 2, and 3. The number 43 is in class 2 because 44 has prime factors 2, 2, and 11, and all of those are in class 1. All </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/525-mersenne-primes\"><w:r><w:t>Mersenne primes</w:t></w:r></w:hyperlink><w:r><w:t> are in class 1, and all </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/45296\"><w:r><w:t>ugly numbers</w:t></w:r></w:hyperlink><w:r><w:t> are in classes 1 or 2. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Write a function to classify prime numbers using this scheme.</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div 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; "><div style="block-size: 144px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 72px; transform-origin: 407px 72px; vertical-align: baseline; "><div 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; "><span 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: 225.233px 7.91667px; transform-origin: 225.233px 7.91667px; unicode-bidi: normal; ">Erdos and Selfridge developed a scheme for classifying a prime number p<span 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: 66.875px 7.91667px; transform-origin: 66.875px 7.91667px; unicode-bidi: normal; ">: If the only factors of <img src="data:image/png;base64,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" alt="p+1" style="width: 36.5px; height: 18px;" width="36.5" height="18"><span 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: 67.6083px 7.91667px; transform-origin: 67.6083px 7.91667px; unicode-bidi: normal; "> are 2 and 3, then put p<span 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: 136.125px 7.91667px; transform-origin: 136.125px 7.91667px; unicode-bidi: normal; "> in class 1. Otherwise, find the largest class r<span 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: 52.1px 7.91667px; transform-origin: 52.1px 7.91667px; unicode-bidi: normal; "> of the factors of <img src="data:image/png;base64,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" alt="p+1" style="width: 36.5px; height: 18px;" width="36.5" height="18"><span 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: 27.225px 7.91667px; transform-origin: 27.225px 7.91667px; unicode-bidi: normal; "> and put p<span 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: 27.225px 7.91667px; transform-origin: 27.225px 7.91667px; unicode-bidi: normal; "> in class <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEQAAAAkCAYAAAAw55zoAAABPUlEQVRoge2YYc3CMBCGHw9zMAMYmAIUzMEczAEW0DAJeMDCNMzCx4+22UHCgPb6jQv3JJeQZbleX9p724HjOI7jOOX0QLt3Ed9AD8zAH3DYuZZd6ViFSGFCkC5Go5jzGKMBJowJUrvY8R/GUMUFecCUIC1hf4+sltUAQ3ymse9NCDIAF5FoIUz+EH+n56fCYsGIIIkkyiUmm4GzGGAsHQBjgiQfH4Er4ZADwdIGfmjLQOgZKdFEWBk59LGoZyG339Z7uagJ0otEM/n3ANmLcmPJnQSKgsgTXknzfHeFnDfeGQrGVxMkuclC3VuiiR7Scf/P1cSEICeNJG9iQpArazOtzdcLIu1W4+D1itqCFK92abedXl1PqSVIQ5iLvGpMZBjEkfLD0CfUEKRl2+pLbLw6Nb6YOY7jOI7jmOMG9q+tsmHOoW8AAAAASUVORK5CYII=" alt="r+1" style="width: 34px; height: 18px;" width="34" height="18"><span 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: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; ">. </div><div 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; "><span 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: 379.108px 7.91667px; transform-origin: 379.108px 7.91667px; unicode-bidi: normal; ">For example, 11 is in class 1 because 12 has prime factors 2, 2, and 3. The number 43 is in class 2 because 44 has prime factors 2, 2, and 11, and all of those are in class 1. All <a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/525-mersenne-primes">Mersenne primes</a><span 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: 69.625px 7.91667px; transform-origin: 69.625px 7.91667px; unicode-bidi: normal; "> are in class 1, and all <a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/45296">ugly numbers</a><span 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: 50.7833px 7.91667px; transform-origin: 50.7833px 7.91667px; unicode-bidi: normal; "> are in classes 1 or 2. </div><div 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; "><span 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: 189.683px 7.91667px; transform-origin: 189.683px 7.91667px; unicode-bidi: normal; ">Write a function to classify prime numbers using this scheme.</div></div></div>

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Problem 51798. Label primes with the Erdos-Selfridge classification

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Problem 51798. Label primes with the Erdos-Selfridge classification

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