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, 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 8px; transform-origin: 368.683px 8px; 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 8px; transform-origin: 7.39167px 8px; 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 8px; transform-origin: 10.5px 8px; 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 8px; transform-origin: 25.2833px 8px; 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 8px; transform-origin: 8.16667px 8px; 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 8px; transform-origin: 25.675px 8px; 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 8px; transform-origin: 8.55px 8px; 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 8px; transform-origin: 20.6167px 8px; 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 8px; transform-origin: 8.16667px 8px; 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 8px; transform-origin: 38.9px 8px; 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 8px; transform-origin: 6.60833px 8px; 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 8px; transform-origin: 19.4417px 8px; 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 8px; transform-origin: 7px 8px; 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 8px; transform-origin: 22.95px 8px; 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 8px; transform-origin: 6.60833px 8px; 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 8px; transform-origin: 20.6083px 8px; 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 8px; transform-origin: 7px 8px; 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 8px; transform-origin: 14.2583px 8px; 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 8px; transform-origin: 6.225px 8px; 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 8px; transform-origin: 24.5083px 8px; 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 8px; transform-origin: 8.16667px 8px; 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 8px; transform-origin: 21.3917px 8px; 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 8px; transform-origin: 8.55px 8px; 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 8px; transform-origin: 19.45px 8px; 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 8px; transform-origin: 7.78333px 8px; 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 8px; transform-origin: 13.0917px 8px; 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 8px; transform-origin: 7.78333px 8px; 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 8px; transform-origin: 26.45px 8px; unicode-bidi: normal; ">back, na<span style="block-size: auto; display: inline; margin-block-end: 0px; 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margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 33.85px 8px; transform-origin: 33.85px 8px; 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 8px; transform-origin: 10.5px 8px; 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 8px; transform-origin: 14.2583px 8px; 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 8px; transform-origin: 7.78333px 8px; 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 8px; transform-origin: 29.175px 8px; 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 8px; transform-origin: 8.16667px 8px; 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 8px; transform-origin: 24.9px 8px; 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 8px; transform-origin: 6.21667px 8px; 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 8px; transform-origin: 38.5px 8px; 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 8px; transform-origin: 363.05px 8px; 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 8px; transform-origin: 1.94167px 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: 1.94167px 8px; transform-origin: 1.94167px 8px; 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 8px; transform-origin: 373.283px 8px; 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 8px; transform-origin: 318.958px 8px; 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 8px; transform-origin: 306.775px 8px; 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 8px; transform-origin: 215.742px 8px; 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 8px; transform-origin: 57.5583px 8px; 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 8px; transform-origin: 82.8583px 8px; 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 8px; transform-origin: 0px 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: 311.567px 8px; transform-origin: 311.567px 8px; 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>

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:
sombrero, dissolution, kidnap, pickpocket, helicopter, birthright, debtor, tawdry, katydid, backdrop, subpoena, anniversary, payback, napkin, mannequin, solemnity, psychosis, lopsided, balderdash, etc. 
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.   
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. 
For example, if the seed is 11, then the list would start 1117, 1171, 2111, 1213, 2131, 1217,… Because the last digits of primes are constrained, 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. 
Write a function to play Outside In with primes: given a two-digit seed , generate a list of  primes following the rules above.

*I devised the game and the name, but I would be surprised if someone had not already thought of it.

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Problem 47518. Play Outside In with primes

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