Problem 46594. Create a sequence of primes p such that p > n π(p)

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>Write a function to find the </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>n</w:t></w:r></w:customXml><w:r><w:t>th term of a sequence of prime numbers </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>p</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:customXmlPr><w:r><w:t>p &gt; n \\pi(p)</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:customXmlPr><w:r><w:t>\\pi(p)</w:t></w:r></w:customXml><w:r><w:t> is the prime counting function. The first three numbers in this sequence are 2, 11, and 37. For example, the second number is 11 because five primes are less than or equal to 11 (i.e., </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>\\pi(11) = 5</w:t></w:r></w:customXml><w:r><w:t>) and 11 &gt; </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>2\\cdot5 = 10</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>A related problem is </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/46117-test-approximations-of-the-prime-counting-function\"><w:r><w:t>Cody Problem 46117</w:t></w:r></w:hyperlink><w:r><w:t> Test approximations of the prime counting function. </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: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 46.5px; transform-origin: 407.5px 46.5px; vertical-align: baseline; "><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: 384.5px 31.5px; text-align: left; transform-origin: 384.5px 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: 83.1px 7.875px; transform-origin: 83.1px 7.875px; unicode-bidi: normal; ">Write a function to find 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: 126.017px 7.875px; transform-origin: 126.017px 7.875px; unicode-bidi: normal; ">th term of a sequence of prime numbers 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: 32.275px 7.875px; transform-origin: 32.275px 7.875px; unicode-bidi: normal; "> such that <img src="data:image/png;base64,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" style="width: 68px; height: 18.5px;" width="68" height="18.5"><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: 24.8917px 7.875px; transform-origin: 24.8917px 7.875px; unicode-bidi: normal; ">, where <img src="data:image/png;base64,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" style="width: 33px; height: 18.5px;" width="33" height="18.5"><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: 40.0583px 7.875px; transform-origin: 40.0583px 7.875px; unicode-bidi: normal; "> is the prime counting function. The first three numbers in this sequence are 2, 11, and 37. For example, the second number is 11 because five primes are less than or equal to 11 (i.e., <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIIAAAAlCAYAAACOGjGrAAAC7klEQVR4nO2a3bWqMBCFdw90QAM2QAVWYAd2QAe2QA2WQA+2YA20cO5D2IdcBEwm3jUT73xr5UUJDmTPXwzgOI7jOI5jiyuARtsIAB2Ak7YR/ysDgIu2ETMNgDvs2POvabUNIANCNEilybxeMrcB8MD3iKE/GKOiXb/kGNLM10/zyEEytwHwRP1p4gLg52Coi72bDUkJTVeEBaTxOUIonfvIuN4iz3mMG2OAgbqMhrzjiiAaemjOYpbMJU+EaFIjjAbqi71HTjSIGSFbzJK5TCk18kAofM1yhyzkagihhZFcmgmdbUQQc6drzisNgoE3wVwNIQAhPZj2rA34vPGYEN77R1rGFsE7jloSjq2K+zwbdRb8tpYQ7sJ5WrQIEXevU5gge/8AgicPBzffGlvK6+fvJKFKSwi0WeJJqU7zbkih425FiOw14AYL2xDeiG0I1Re3KXsdwX2+VoK2EErEWzI+FY06LN0T1yuroxix7MidsIiAXOfPUpTLFyNBSwgsvCQF4ycignQndQs6NcWQnCIa/J3rmR5i46iylF24moVQ637CGjqztGj/rfjjfMmbPhPv4UKwAaOCqBtiCojTwg15yqpRCCWdjlVY94iEwBQQewb38VMLKaYWCTUWi9pdwx58puzUwPAY1wL0lAnp1WfN7aNkz95S1xBDh8yOcnygeGv4vvHZu52rkgpcSwgj0mugNda6BiAIekJm+9hiWfD1AjJV8CWl/m3Lrc5ctIQwIe2fUitQfHtRlxEu2RnjdLD2fGA7jKWE/AEyD2OlK1lM6Vy+A3N/2uywXrP1mQMW/FlRJj7dMuF1nyCOFDk3z325LRYVc/RIC2slcwG5aDVZ1yUTlvT2gPDU1RlhgbfyPs8A9jvfvzM2Jdx2OM6fR8VOyVxgyaU1to0nvD6ryWN3LcJLthxybzByuPPbuSCEKotHqTrktcVOIT3sVeTfcoK5Oi6wI4YGIR24CJTgaWNtrNjhOI7jOI7jODb5Ax+QqaGPbwHFAAAAAElFTkSuQmCC" style="width: 65px; height: 18.5px;" width="65" height="18.5"><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: 33.1333px 7.875px; transform-origin: 33.1333px 7.875px; unicode-bidi: normal; ">) and 11 &gt; <img src="data:image/png;base64,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" style="width: 62.5px; height: 18px;" width="62.5" 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: 3.88333px 7.875px; transform-origin: 3.88333px 7.875px; 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: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 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: 64.1833px 7.875px; transform-origin: 64.1833px 7.875px; unicode-bidi: normal; ">A related problem is <a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/46117-test-approximations-of-the-prime-counting-function">Cody Problem 46117</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: 161.808px 7.875px; transform-origin: 161.808px 7.875px; unicode-bidi: normal; "> Test approximations of the prime counting function. </div></div></div>

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Problem 46594. Create a sequence of primes p such that p > n π(p)

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Problem 46594. Create a sequence of primes p such that p > n π(p)

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