Problem 51758. List Proth primes

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>As of datenum 738289, three of the </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Largest_known_prime_number#The_twenty_largest_known_prime_numbers\"><w:r><w:rPr><w:u/></w:rPr><w:t>twenty largest known prime numbers</w:t></w:r></w:hyperlink><w:r><w:t> are Proth primes, prime numbers of the form </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=\"k 2^m+1\"/></w:customXmlPr><w:r><w:t>k\\cdot 2^m + 1</w:t></w:r></w:customXml><w:r><w:t> with </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=\"k &lt;= 2^m\"/></w:customXmlPr><w:r><w:t>k \\le 2^m</w:t></w:r></w:customXml><w:r><w:t>. For example, taking </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=\"k = 1\"/></w:customXmlPr><w:r><w:t>k = 1</w:t></w:r></w:customXml><w:r><w:t> and </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=\"m = 1\"/></w:customXmlPr><w:r><w:t>m = 1</w:t></w:r></w:customXml><w:r><w:t> gives 3, the first Proth prime, and taking </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=\"k = 3\"/></w:customXmlPr><w:r><w:t>k = 3</w:t></w:r></w:customXml><w:r><w:t> and </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=\"m = 5\"/></w:customXmlPr><w:r><w:t>m = 5</w:t></w:r></w:customXml><w:r><w:t> gives 97, the sixth Proth prime. The number 199 is prime but not a Proth prime because </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=\"k = 99 &gt; 2^m = 2\"/></w:customXmlPr><w:r><w:t>k = 99 &gt; 2^m = 2</w:t></w:r></w:customXml><w:r><w:t>. The number 49 is a Proth 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=\"k = 3\"/></w:customXmlPr><w:r><w:t>k = 3</w:t></w:r></w:customXml><w:r><w:t>, </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=\"m = 4\"/></w:customXmlPr><w:r><w:t>m = 4</w:t></w:r></w:customXml><w:r><w:t>) but not prime.</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 list the Proth primes between two limits </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=\"a\"/></w:customXmlPr><w:r><w:t>a</w:t></w:r></w:customXml><w:r><w:t> and </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=\"b\"/></w:customXmlPr><w:r><w:t>b</w:t></w:r></w:customXml><w:r><w:t>. Also provide the values 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=\"k\"/></w:customXmlPr><w:r><w:t>k</w:t></w:r></w:customXml><w:r><w:t> and </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=\"m\"/></w:customXmlPr><w:r><w:t>m</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>Optional: Values 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=\"k\"/></w:customXmlPr><w:r><w:t>k</w:t></w:r></w:customXml><w:r><w:t> for which no values 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=\"k 2^m + 1\"/></w:customXmlPr><w:r><w:t>k\\cdot 2^m + 1</w:t></w:r></w:customXml><w:r><w:t> are prime are called Sierpinski numbers. Show that 78,557 is the smallest Sierpinski number. For more, see </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Sierpi%C5%84ski_number#Sierpi%C5%84ski_problem\"><w:r><w:rPr><w:u/></w:rPr><w:t>this page</w:t></w:r></w:hyperlink><w:r><w:t>. </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: 165px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 82.5px; transform-origin: 407px 82.5px; vertical-align: baseline; "><div style="block-size: 84px; 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 42px; text-align: left; transform-origin: 384px 42px; 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: 111.625px 7.91667px; transform-origin: 111.625px 7.91667px; unicode-bidi: normal; ">As of datenum 738289, three of the <a target='_blank' href = "https://en.wikipedia.org/wiki/Largest_known_prime_number#The_twenty_largest_known_prime_numbers">twenty largest known prime 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: 141.567px 7.91667px; transform-origin: 141.567px 7.91667px; unicode-bidi: normal; "> are Proth primes, prime numbers of the form <img src="data:image/png;base64,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" alt="k 2^m+1" style="width: 60px; height: 19.5px;" width="60" height="19.5"><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: 16.3333px 7.91667px; transform-origin: 16.3333px 7.91667px; unicode-bidi: normal; "> with <img src="data:image/png;base64,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" alt="k <= 2^m" style="width: 43.5px; height: 19.5px;" width="43.5" height="19.5"><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: 67.2833px 7.91667px; transform-origin: 67.2833px 7.91667px; unicode-bidi: normal; ">. For example, taking <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEgAAAAkCAYAAAAq23xmAAABcUlEQVRoge2YYa2DMBSFPw84qAEMoAAFOJgDHMwCGiZhHrAwDbOw96NtuCPjLezepNDcL2kWyjiUA5xbCo7jOI5TIy3QASMwAY+0XQsdyuvpiea8UnsCjX5cxemAO/GaLhaCjyR2txArSGAxJje1QY2lWEECcfz51+yaeiHWasUOQoehQVeW/KkFU4PmJHTTCh0IM4PCB6HAUh5lOxNmBg1CKKS+wJJLz50nCMRpg7Zpb4iZQVMSeaz6L8RXb++cSA5M07S5YWZQnv9Mom/g9zyyeoK01dTEoFaIDKlv1AgeCBOD5GSqJT41079HnAcTg24s+ZNL/WwxugNgYpD8QJ3FtqaCVFPFpMDAex5pJozVVDG5xJFLufwKDhvHfaOaKpZfKbm8ISeN19TX8Nt8qDQqg+Tyxrjat86i6cN/zoBcodhtkDx4HYYtMbQt8qgUPe83emZn6Oc16K0nI+fIsLH/yHzLtrNFheM4juM4jlOSP3ic0uxUzyx9AAAAAElFTkSuQmCC" alt="k = 1" style="width: 36px; height: 18px;" width="36" 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: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; "> and <img src="data:image/png;base64,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" alt="m = 1" style="width: 40px; height: 18px;" width="40" 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: 127.175px 7.91667px; transform-origin: 127.175px 7.91667px; unicode-bidi: normal; "> gives 3, the first Proth prime, and taking <img src="data:image/png;base64,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" alt="k = 3" style="width: 36px; height: 18px;" width="36" 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: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; "> and <img src="data:image/png;base64,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" alt="m = 5" style="width: 40px; height: 18px;" width="40" 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: 1.94167px 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; "> gives 97, the sixth Proth prime. The number 199 is prime but not a Proth prime because <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAM4AAAAnCAYAAABHVHeOAAAER0lEQVR4nO2c65GrOhCEOwdn4AScABE4AjLYDJzBpkAMDsE5OAXHQAp7f4guBlk8xGAjzu2vijq7XoZCj54ZaeQDCCGEEEIIIYQQQgghhBBCiCNzBlB3/wohJrgBeAD4M9eRhXMB0CC06QGgBXAHcP2wbYlUCO/foh/bB6bbc+n+Xne/nxHmyE90T/xZ6dQYznOO7cX74Ff3wCeAk/dhO/GD0AY7oCcEMXDSfMK2RH4xdIbx9ZuwuSGM/1/3c40wLzg3zp0dnUqL8p3sCe+BIb5cjpEPaVyvuR81euHHnNAPfqp9HtsSuSK8L6NlhXePGzsJwnuYiQChX9rusxtCnzCKlc4vwrs2CP1QIbSbY8prVeS5YCP17YQdyNvIPYwocSd5bEulRTqiAMO2vEZsWwydCO+9d79TmKVH4QtCW+qRv9/hDBi2M4+YpjFi/CF4lBTWOdhO8tgu4Y5xQX6CGvPptvW2NtWy7aSDqNCvCQjTwG+2aw0NpsfrjGknMguVl0pVjgDXIXMRwS4Mt7BdAlMfpjqfpsG4hyV2/WPbTAfaJO617842jTmaUnhiPkPgmi53XAH0qcpYeC8dm7tPdZTdXaKn9dgu4YyhOCmgPSP7zbyLbUtKEJxY9n3Zln8Btjk7aDAU2w6r0O+ePNAvrErFTv6p90yJxGObQywgevY9BMQoEk+W2POe8L6WqcxnNcpP1+agY8gOGtb72EFk/pfrHa0QPVdOjcCmHlMDmZr8Hts1lCAgThab0nHBbycQ13+2Xzhf7ug3C5ZAO++15eYMHUO75rmcENarcO97zQ7bHsLhoM+F3CfeB8Bj62EvAdEhxm2tECa3Td2uic9Y/MzNQEoUDh1DdrSh4qxXYdGv5NQshZ3YqcWx3TGKPYzH1su3BdQgtOFo4/sJWNzN7mvrbSuECfFA+dXgFNyzt5OPBa8GQ3HEOyge260YE9CWIq0wXdf4P3FDEM2q/mV+/0J6K/JonBDaZCf6A31qYSfklrZbcsVQxC9sEx1Y6D3qzumWuB1IfOyA1xGLoHNYb567dvPYLqXCcAPiieDMthiLU/c8iSZEmBccorFV0wbD0wOeU697bA7MYduae0zEY7uElGC2TKVKEU0JmwNu0QDDoyYXDM9sefL4EoVjq/e5He+xnYInjz8lGGC5aL6RYewtnCWiWdQPTD/sroKtadiU5MiLSVunym2Hx3aMbwiGNJivtfzg+EXMOehA5pzxHQvWk4wudrGbOvTGVOKI656SRBMLZtEgOeC2M79WkLpuOMZ3ajxQNE+M9wO/8Dd77MbWJeJJYUPqA44tux05Y3hwNef9PbYprviuYID3be2pK6f6fzQoms2WB3YjIOVt7Db1kQplrLu06M9SfcN2Cq6RviEYYP6bn/F1xO9fLSVHNP965B2FNZc1/9mIx3aONcdThBBCCCGEEEIIIYQQQgghhBBCiG35D29QvfiypAyqAAAAAElFTkSuQmCC" alt="k = 99 > 2^m = 2" style="width: 103px; height: 19.5px;" width="103" height="19.5"><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: 59.075px 7.91667px; transform-origin: 59.075px 7.91667px; unicode-bidi: normal; ">. The number 49 is a Proth number (<img src="data:image/png;base64,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" alt="k = 3" style="width: 36px; height: 18px;" width="36" 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; ">, <img src="data:image/png;base64,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" alt="m = 4" style="width: 40px; height: 18px;" width="40" 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: 47.0583px 7.91667px; transform-origin: 47.0583px 7.91667px; unicode-bidi: normal; ">) but not prime.</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: 181.117px 7.91667px; transform-origin: 181.117px 7.91667px; unicode-bidi: normal; ">Write a function to list the Proth primes between two limits 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: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; "> and b<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: 85.9583px 7.91667px; transform-origin: 85.9583px 7.91667px; unicode-bidi: normal; ">. Also provide the values of k<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: 15.5583px 7.91667px; transform-origin: 15.5583px 7.91667px; unicode-bidi: normal; "> and m<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: 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: 60.55px 7.91667px; transform-origin: 60.55px 7.91667px; unicode-bidi: normal; ">Optional: Values of k<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: 71.5667px 7.91667px; transform-origin: 71.5667px 7.91667px; unicode-bidi: normal; "> for which no values of <img src="data:image/png;base64,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" alt="k 2^m + 1" style="width: 60px; height: 19.5px;" width="60" height="19.5"><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: 204.217px 7.91667px; transform-origin: 204.217px 7.91667px; unicode-bidi: normal; "> are prime are called Sierpinski numbers. Show that 78,557 is the smallest Sierpinski number. For more, see <a target='_blank' href = "https://en.wikipedia.org/wiki/Sierpi%C5%84ski_number#Sierpi%C5%84ski_problem">this page</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: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; ">. </div></div></div>

Solve

Solution Stats

19 Solutions
10 Solvers

Last Solution submitted on May 02, 2023

Last 200 Solutions

Problem Comments

3 Comments

3 Comments

Dyuman Joshi on 2 Jun 2022

Chris, what if there are multiple pairs of (k,m) that result in a particular proth number, which pair should we report?

For example -

k=4, m=2, p=17
k=2, m=3, p=17
k=1, m=4, p=17

also
k=1, m=2, p=5
k=2, m=1, p=5

ChrisR on 7 Jun 2022

Good question, Dyuman. Please use the largest m possible.

Dyuman Joshi on 17 Jun 2022

Thanks for the clarification, Chris.
Nice question!

Solution Comments

Show comments

Problem Recent Solvers10

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 51758. List Proth primes

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers10

Suggested Problems

More from this Author207

Problem Tags

Community Treasure Hunt

Problem 51758. List Proth primes

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers10

Suggested Problems

More from this Author207

Problem Tags

Community Treasure Hunt

Players