Problem 46057. Find the last non-zero digit in a primorial

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:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/groups/2001/problems/45251\"><w:r><w:t>Cody Problem 45251</w:t></w:r></w:hyperlink><w:r><w:t> asked us to find the last non-zero digit in a factorial. For this problem consider the primorial </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_n\"/></w:customXmlPr><w:r><w:t>p_n</w:t></w:r></w:customXml><w:r><w:t>#, the product of primes up to and including 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 </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_n\"/></w:customXmlPr><w:r><w:t>p_n</w:t></w:r></w:customXml><w:r><w:t>. For example, for </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> = 12, the primorial is 7420738134810, whose last non-zero digit is 1.</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>Find the last non-zero digit in the primorial </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_n\"/></w:customXmlPr><w:r><w:t>p_n</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>See also</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/46054-count-trailing-zeros-in-a-primorial\"><w:r><w:t>Cody Problems 46054</w:t></w:r></w:hyperlink><w:r><w:t> \"Count trailing zeros in a primorial\" and </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/46060-identify-primorial-primes\"><w:r><w:t>46060 \"Identify primorial primes\"</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: 123.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 61.8833px; transform-origin: 407px 61.8833px; vertical-align: baseline; "><div style="block-size: 63.5px; 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 31.75px; text-align: left; transform-origin: 384px 31.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/groups/2001/problems/45251">Cody Problem 45251</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: 284.733px 7.91667px; transform-origin: 284.733px 7.91667px; unicode-bidi: normal; "> asked us to find the last non-zero digit in a factorial. For this problem consider the primorial <img src="data:image/png;base64,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" alt="p_n" style="width: 15.5px; height: 20px;" width="15.5" height="20"><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: 19.45px 7.91667px; transform-origin: 19.45px 7.91667px; unicode-bidi: normal; ">#, the product of primes up to and including 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: 27.2333px 7.91667px; transform-origin: 27.2333px 7.91667px; unicode-bidi: normal; ">th prime <img src="data:image/png;base64,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" alt="p_n" style="width: 15.5px; height: 20px;" width="15.5" height="20"><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: 56.7833px 7.91667px; transform-origin: 56.7833px 7.91667px; unicode-bidi: normal; ">. For example, for 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: 143.75px 7.91667px; transform-origin: 143.75px 7.91667px; unicode-bidi: normal; "> = 12, the primorial is 7420738134810, whose last non-zero digit is 1.</div><div style="block-size: 21.25px; 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 10.6333px; text-align: left; transform-origin: 384px 10.6333px; 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: 132.267px 7.91667px; transform-origin: 132.267px 7.91667px; unicode-bidi: normal; ">Find the last non-zero digit in the primorial <img src="data:image/png;base64,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" alt="p_n" style="width: 15.5px; height: 20px;" width="15.5" height="20"><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: 5.83333px 7.91667px; transform-origin: 5.83333px 7.91667px; 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: 27.2333px 7.91667px; transform-origin: 27.2333px 7.91667px; unicode-bidi: normal; ">See also<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 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; "> <a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/46054-count-trailing-zeros-in-a-primorial">Cody Problems 46054</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: 124.783px 7.91667px; transform-origin: 124.783px 7.91667px; unicode-bidi: normal; "> "Count trailing zeros in a primorial" and <a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/46060-identify-primorial-primes">46060 "Identify primorial 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: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; ">.</div></div></div>

Solve

Solution Stats

19 Solutions
7 Solvers

Last Solution submitted on Jan 25, 2021

Last 200 Solutions

Problem Comments

Problem Recent Solvers7

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 46057. Find the last non-zero digit in a primorial

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers7

Suggested Problems

More from this Author67

Problem Tags

Community Treasure Hunt

Problem 46057. Find the last non-zero digit in a primorial

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers7

Suggested Problems

More from this Author67

Problem Tags

Community Treasure Hunt

Players