Problem 51798. Label primes with the Erdos-Selfridge classification

Created by ChrisR

Solve Later

{"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>

Solve

Solution Stats

14 Solutions
8 Solvers

Last Solution submitted on Mar 01, 2022

Last 200 Solutions

Problem Comments

Problem Recent Solvers8

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 51798. Label primes with the Erdos-Selfridge classification

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers8

Suggested Problems

More from this Author165

Problem Tags

Community Treasure Hunt

Problem 51798. Label primes with the Erdos-Selfridge classification

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers8

Suggested Problems

More from this Author165

Problem Tags

Community Treasure Hunt

Players