Problem 45964. Compute the nth Pythagorean prime

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>Pythagorean primes have 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=\"p = 4n+1\"/></w:customXmlPr><w:r><w:t>p = 4n+1</w:t></w:r></w:customXml><w:r><w:t>, where </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=\"n\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t> is an integer, and they can be written as the sum of squares of two integers. More information is available at</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Pythagorean_prime\"><w:r><w:t>Wikipedia</w:t></w:r></w:hyperlink><w:r><w:t>,</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.youtube.com/watch?v=yu_aqA7mw7E\"><w:r><w:t>Numberphile</w:t></w:r></w:hyperlink><w:r><w:t>, and the</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://oeis.org/A002144\"><w:r><w:t>Online Encyclopedia of Integer Sequences</w:t></w:r></w:hyperlink><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>Compute the </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=\"n\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t>th Pythagorean prime </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> and two integers </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> such that </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 = a^2+b^2\"/></w:customXmlPr><w:r><w:t>p = a^2+b^2</w:t></w:r></w:customXml><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: 72px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 36px; transform-origin: 407px 36px; 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: 109.3px 7.8px; transform-origin: 109.3px 7.8px; unicode-bidi: normal; ">Pythagorean primes have the form <img src="data:image/png;base64,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" alt="p = 4n+1" style="width: 70px; height: 18px;" width="70" 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: 24.9px 7.8px; transform-origin: 24.9px 7.8px; unicode-bidi: normal; ">, where n<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: 209.25px 7.8px; transform-origin: 209.25px 7.8px; unicode-bidi: normal; "> is an integer, and they can be written as the sum of squares of two integers. More information is available at<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: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; "> <a target='_blank' href = "https://en.wikipedia.org/wiki/Pythagorean_prime">Wikipedia</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: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; ">,<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: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; "> <a target='_blank' href = "https://www.youtube.com/watch?v=yu_aqA7mw7E">Numberphile</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: 27.2333px 7.8px; transform-origin: 27.2333px 7.8px; unicode-bidi: normal; ">, and the<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: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; "> <a target='_blank' href = "https://oeis.org/A002144">Online Encyclopedia of Integer Sequences</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: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; ">.</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: 42.0167px 7.8px; transform-origin: 42.0167px 7.8px; unicode-bidi: normal; ">Compute the n<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: 68.85px 7.8px; transform-origin: 68.85px 7.8px; unicode-bidi: normal; ">th Pythagorean prime 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: 55.2333px 7.8px; transform-origin: 55.2333px 7.8px; unicode-bidi: normal; "> and two integers 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: 15.5667px 7.8px; transform-origin: 15.5667px 7.8px; 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: 32.2833px 7.8px; transform-origin: 32.2833px 7.8px; unicode-bidi: normal; "> such that <img src="data:image/png;base64,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" alt="p = a^2+b^2" style="width: 72.5px; height: 19px;" width="72.5" height="19"><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: 1.95px 7.8px; transform-origin: 1.95px 7.8px; unicode-bidi: normal; ">.</div></div></div>

Solve

Solution Stats

64 Solutions
25 Solvers

Last Solution submitted on Aug 17, 2023

Last 200 Solutions

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers25

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 45964. Compute the nth Pythagorean prime

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers25

Suggested Problems

More from this Author218

Problem Tags

Community Treasure Hunt

Problem 45964. Compute the nth Pythagorean prime

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers25

Suggested Problems

More from this Author218

Problem Tags

Community Treasure Hunt

Players