Problem 52183. List the nth prime quartet prefix

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>Prime numbers larger than 5 can end only in 1, 3, 7, or 9, but of course not all numbers ending in these four digits are prime. Let’s call a group of four prime numbers between </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=\"10k\"/></w:customXmlPr><w:r><w:t>10k</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=\"10(k+1)\"/></w:customXmlPr><w:r><w:t>10(k+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\"/></w:customXmlPr><w:r><w:t>k</w:t></w:r></w:customXml><w:r><w:t> an integer 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=\"k &gt;= 1\"/></w:customXmlPr><w:r><w:t>k\\ge 1</w:t></w:r></w:customXml><w:r><w:t>) a </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>prime quartet</w:t></w:r><w:r><w:t>. The first one is 11, 13, 17, and 19, and the second is 101, 103, 107, and 109. Therefore, the prefix (or the number excluding the last digit) of the first prime quartet is 1, and the prefix of the second prime quartet is 10.</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 that returns 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 prime quartet prefix. </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: Prove that the sequence of prime quartet prefixes is infinite. Just drop your proof in the comments below. </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: 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: 372.5px 8px; transform-origin: 372.5px 8px; unicode-bidi: normal; "><span style="">Prime numbers larger than 5 can end only in 1, 3, 7, or 9, but of course not all numbers ending in these four digits are prime. Let’s call a group of four prime numbers between </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="10k" style="width: 25px; height: 18px;" width="25" height="18"></span><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: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; "><span style=""> and </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="10(k+1)" style="width: 61px; height: 18.5px;" width="61" height="18.5"></span><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: 18.5px 8px; transform-origin: 18.5px 8px; unicode-bidi: normal; "><span style=""> (with </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">k</span><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: 50px 8px; transform-origin: 50px 8px; unicode-bidi: normal; "><span style=""> an integer and </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="k >= 1" style="width: 36px; height: 18px;" width="36" height="18"></span><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: 10.5px 8px; transform-origin: 10.5px 8px; unicode-bidi: normal; "><span style="">) a </span></span><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: 42px 8px; transform-origin: 42px 8px; unicode-bidi: normal; "><span style="font-style: italic; ">prime quartet</span></span><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: 3.46667px 8px; transform-origin: 3.46667px 8px; unicode-bidi: normal; "><span style="">. The first one is 11, 13, 17, and 19, and the second is 101, 103, 107, and 109. Therefore, the prefix (or the number excluding the last digit) of the first prime quartet is 1, and the prefix of the second prime quartet is 10.</span></span></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: 102px 8px; transform-origin: 102px 8px; unicode-bidi: normal; "><span style="">Write a function that returns the </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">n</span><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: 73px 8px; transform-origin: 73px 8px; unicode-bidi: normal; "><span style="">th prime quartet prefix. </span></span></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: 360.5px 8px; transform-origin: 360.5px 8px; unicode-bidi: normal; "><span style="">Optional: Prove that the sequence of prime quartet prefixes is infinite. Just drop your proof in the comments below. </span></span></div></div></div>

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Problem 52183. List the nth prime quartet prefix

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Problem 52183. List the nth prime quartet prefix

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