Problem 47518. Play Outside In with 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>In the word game Outside In,* you start with a word, take the first and last letters, try to think of a word in which the two letters appear together in the interior, and repeat. For example, starting with ‘MATLAB’, you might proceed as follows:</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>so</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>mb</w:t></w:r><w:r><w:t>rero, dis</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>so</w:t></w:r><w:r><w:t>lution, ki</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>dn</w:t></w:r><w:r><w:t>ap, pic</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>kp</w:t></w:r><w:r><w:t>ocket, helico</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>pt</w:t></w:r><w:r><w:t>er, birt</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>hr</w:t></w:r><w:r><w:t>ight, de</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>bt</w:t></w:r><w:r><w:t>or, taw</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>dr</w:t></w:r><w:r><w:t>y, ka</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>ty</w:t></w:r><w:r><w:t>did, bac</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>kd</w:t></w:r><w:r><w:t>rop, su</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>bp</w:t></w:r><w:r><w:t>oena, anniver</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>sa</w:t></w:r><w:r><w:t>ry, p</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>ay</w:t></w:r><w:r><w:t>back, na</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>pk</w:t></w:r><w:r><w:t>in, tu</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>nn</w:t></w:r><w:r><w:t>el, ma</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>nn</w:t></w:r><w:r><w:t>equin, sole</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>mn</w:t></w:r><w:r><w:t>ity, p</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>sy</w:t></w:r><w:r><w:t>chosis, lo</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>ps</w:t></w:r><w:r><w:t>ided, ba</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>ld</w:t></w:r><w:r><w:t>erdash, etc. </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>You can play alone or with others, and you could add other rules or objectives—e.g., all words must have six or more letters, a person who cannot think of a word is eliminated, players try to generate a list that uses all letters in the alphabet, etc. </w:t></w:r><w:r><w:t> </w:t></w:r><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>This game has one problem: without a convenient and stable word list, it does not translate easily to Cody. So instead of words, let’s use prime numbers. In particular, start with a two-digit seed, find the smallest prime for which the two digits appear together in the interior, create a new two-digit number from the first and last digits of the prime, and repeat. </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>For example, if the seed is 11, then the list would start 1117, 1171, 2111, 1213, 2131, 1217,… Because </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/45994-investigate-the-frequency-of-last-digits-of-prime-numbers\"><w:r><w:t>the last digits of primes are constrained</w:t></w:r></w:hyperlink><w:r><w:t>, you will notice similarities in lists generated from different seeds. Solvers able to plot the numbers might enjoy seeing the patterns for longer lists graphically. </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 play Outside In with primes: given a two-digit seed </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>x</w:t></w:r></w:customXml><w:r><w:t>, generate a list of </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> primes following the rules above. </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></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>*I devised the game and the name, but I would be surprised if someone had not already thought of it.</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: 420px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 210px; transform-origin: 407px 210px; 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: 368.683px 7.79167px; transform-origin: 368.683px 7.79167px; unicode-bidi: normal; ">In the word game Outside In,* you start with a word, take the first and last letters, try to think of a word in which the two letters appear together in the interior, and repeat. For example, starting with ‘MATLAB’, you might proceed as follows:</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: 7.39167px 7.79167px; transform-origin: 7.39167px 7.79167px; unicode-bidi: normal; ">so<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 7.79167px; transform-origin: 10.5px 7.79167px; unicode-bidi: normal; ">mb<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: 25.2833px 7.79167px; transform-origin: 25.2833px 7.79167px; unicode-bidi: normal; ">rero, dis<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: 8.16667px 7.79167px; transform-origin: 8.16667px 7.79167px; unicode-bidi: normal; ">so<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: 25.675px 7.79167px; transform-origin: 25.675px 7.79167px; unicode-bidi: normal; ">lution, ki<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: 8.55px 7.79167px; transform-origin: 8.55px 7.79167px; unicode-bidi: normal; ">dn<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: 20.6167px 7.79167px; transform-origin: 20.6167px 7.79167px; unicode-bidi: normal; ">ap, pic<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: 8.16667px 7.79167px; transform-origin: 8.16667px 7.79167px; unicode-bidi: normal; ">kp<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: 38.9px 7.79167px; transform-origin: 38.9px 7.79167px; unicode-bidi: normal; ">ocket, helico<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: 6.60833px 7.79167px; transform-origin: 6.60833px 7.79167px; unicode-bidi: normal; ">pt<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: 19.4417px 7.79167px; transform-origin: 19.4417px 7.79167px; unicode-bidi: normal; ">er, birt<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: 7px 7.79167px; transform-origin: 7px 7.79167px; unicode-bidi: normal; ">hr<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: 22.95px 7.79167px; transform-origin: 22.95px 7.79167px; unicode-bidi: normal; ">ight, de<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: 6.60833px 7.79167px; transform-origin: 6.60833px 7.79167px; unicode-bidi: normal; ">bt<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: 20.6083px 7.79167px; transform-origin: 20.6083px 7.79167px; unicode-bidi: normal; ">or, taw<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: 7px 7.79167px; transform-origin: 7px 7.79167px; unicode-bidi: normal; ">dr<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: 14.2583px 7.79167px; transform-origin: 14.2583px 7.79167px; unicode-bidi: normal; ">y, ka<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: 6.225px 7.79167px; transform-origin: 6.225px 7.79167px; unicode-bidi: normal; ">ty<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: 24.5083px 7.79167px; transform-origin: 24.5083px 7.79167px; unicode-bidi: normal; ">did, bac<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: 8.16667px 7.79167px; transform-origin: 8.16667px 7.79167px; unicode-bidi: normal; ">kd<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: 21.3917px 7.79167px; transform-origin: 21.3917px 7.79167px; unicode-bidi: normal; ">rop, su<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: 8.55px 7.79167px; transform-origin: 8.55px 7.79167px; unicode-bidi: normal; ">bp<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 7.79167px; transform-origin: 19.45px 7.79167px; unicode-bidi: normal; ">oena, anniver<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: 7.78333px 7.79167px; transform-origin: 7.78333px 7.79167px; unicode-bidi: normal; ">sa<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: 13.0917px 7.79167px; transform-origin: 13.0917px 7.79167px; unicode-bidi: normal; ">ry, 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: 7.78333px 7.79167px; transform-origin: 7.78333px 7.79167px; unicode-bidi: normal; ">ay<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: 26.45px 7.79167px; transform-origin: 26.45px 7.79167px; unicode-bidi: normal; ">back, na<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: 8.16667px 7.79167px; transform-origin: 8.16667px 7.79167px; unicode-bidi: normal; ">pk<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: 15.1667px 7.79167px; transform-origin: 15.1667px 7.79167px; unicode-bidi: normal; ">in, tu<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: 8.55px 7.79167px; transform-origin: 8.55px 7.79167px; unicode-bidi: normal; ">nn<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: 19.0583px 7.79167px; transform-origin: 19.0583px 7.79167px; unicode-bidi: normal; ">el, ma<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: 8.55px 7.79167px; transform-origin: 8.55px 7.79167px; unicode-bidi: normal; ">nn<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: 33.85px 7.79167px; transform-origin: 33.85px 7.79167px; unicode-bidi: normal; ">equin, sole<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 7.79167px; transform-origin: 10.5px 7.79167px; unicode-bidi: normal; ">mn<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: 14.2583px 7.79167px; transform-origin: 14.2583px 7.79167px; unicode-bidi: normal; ">ity, 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: 7.78333px 7.79167px; transform-origin: 7.78333px 7.79167px; unicode-bidi: normal; ">sy<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: 29.175px 7.79167px; transform-origin: 29.175px 7.79167px; unicode-bidi: normal; ">chosis, lo<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: 8.16667px 7.79167px; transform-origin: 8.16667px 7.79167px; unicode-bidi: normal; ">ps<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 7.79167px; transform-origin: 24.9px 7.79167px; unicode-bidi: normal; ">ided, ba<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: 6.21667px 7.79167px; transform-origin: 6.21667px 7.79167px; unicode-bidi: normal; ">ld<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: 38.5px 7.79167px; transform-origin: 38.5px 7.79167px; unicode-bidi: normal; ">erdash, etc. </div><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: 384px 31.5px; text-align: left; transform-origin: 384px 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: 363.05px 7.79167px; transform-origin: 363.05px 7.79167px; unicode-bidi: normal; ">You can play alone or with others, and you could add other rules or objectives—e.g., all words must have six or more letters, a person who cannot think of a word is eliminated, players try to generate a list that uses all letters in the alphabet, etc. <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 7.79167px; transform-origin: 1.94167px 7.79167px; 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: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; "> </div><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: 384px 31.5px; text-align: left; transform-origin: 384px 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: 373.283px 7.79167px; transform-origin: 373.283px 7.79167px; unicode-bidi: normal; ">This game has one problem: without a convenient and stable word list, it does not translate easily to Cody. So instead of words, let’s use prime numbers. In particular, start with a two-digit seed, find the smallest prime for which the two digits appear together in the interior, create a new two-digit number from the first and last digits of the prime, and repeat. </div><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: 384px 31.5px; text-align: left; transform-origin: 384px 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: 318.958px 7.79167px; transform-origin: 318.958px 7.79167px; unicode-bidi: normal; ">For example, if the seed is 11, then the list would start 1117, 1171, 2111, 1213, 2131, 1217,… Because <a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/45994-investigate-the-frequency-of-last-digits-of-prime-numbers">the last digits of primes are constrained</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: 306.775px 7.79167px; transform-origin: 306.775px 7.79167px; unicode-bidi: normal; ">, you will notice similarities in lists generated from different seeds. Solvers able to plot the numbers might enjoy seeing the patterns for longer lists graphically. </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: 215.742px 7.79167px; transform-origin: 215.742px 7.79167px; unicode-bidi: normal; ">Write a function to play Outside In with primes: given a two-digit seed x<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: 57.5583px 7.79167px; transform-origin: 57.5583px 7.79167px; unicode-bidi: normal; ">, generate a list of 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: 82.8583px 7.79167px; transform-origin: 82.8583px 7.79167px; unicode-bidi: normal; "> primes following the rules above. </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: 0px 7.79167px; transform-origin: 0px 7.79167px; 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: 311.567px 7.79167px; transform-origin: 311.567px 7.79167px; unicode-bidi: normal; ">*I devised the game and the name, but I would be surprised if someone had not already thought of it.</div></div></div>

Solve

Solution Stats

9 Solutions
6 Solvers

Last Solution submitted on Feb 05, 2022

Last 200 Solutions

Problem Recent Solvers6

Problem Tags

primes puzzle sequence

Community Treasure Hunt

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

Start Hunting!

Problem 47518. Play Outside In with primes

Solution Stats

Last 200 Solutions

Problem Recent Solvers6

Suggested Problems

More from this Author147

Problem Tags

Community Treasure Hunt

Problem 47518. Play Outside In with primes

Solution Stats

Last 200 Solutions

Problem Recent Solvers6

Suggested Problems

More from this Author147

Problem Tags

Community Treasure Hunt

Players