Problem 44343. Pair Primes

Created by Mehmet OZC

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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>Let's define pair primes as follow;</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>For 2 digits numbers:</w:t></w:r><w:r><w:t> 11 and 17 are pair primes because both of them are 2 digits prime numbers and last digit of the first prime equals to the first digit of second prime number. 11 and 11 are not pair primes because a = b.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>For 3 digit numbers:</w:t></w:r><w:r><w:t> 389 and 967 are pair primes because both of them are 3 digits prime numbers and last digit of the first prime equals to the first digit of the second prime number (797 and 797 are not pair primes because a = b). 467 and 673 are pair primes too because the last two digits of the first prime number (67) equals to the first two digit (67) of the second prime number. 211 and 113 are pair primes too but they satisfy two conditions: last digit of the first prime equals to the first digit of the second prime also last two digits of the first prime equals to the first two digits of the first prime.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>For 4 digit numbers:</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>1-) 1637 and 7549 are pair primes. First ends with 7 and second starts with 7.</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>2-) 6221 and 2113 are pair primes. First ends with 21 and second starts with 21.</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>3-) 1429 and 4297 are pair primes. First ends with 429 and second starts with 429. You should be careful. 2111 and 1117 are also four digit pair primes. It satisfies three conditions. First ends with 1 and second starts with 1. First ends with 11 and second starts with 11. First ends with 111 and second starts with 111. [2111 1117] pair should be counted for once.</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>Given the digit counts, can you determine how many unique pair primes are there (a~=b)</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: 387.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 193.95px; transform-origin: 407px 193.95px; vertical-align: baseline; "><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: 104.5px 8px; transform-origin: 104.5px 8px; unicode-bidi: normal; "><span style="">Let's define pair primes as follow;</span></span></div><ul style="block-size: 183.9px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 91.95px; transform-origin: 391px 91.95px; margin-top: 10px; margin-bottom: 20px; "><li style="block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4333px; text-align: left; transform-origin: 363px 20.4333px; white-space: pre-wrap; margin-left: 56px; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 74.5px 8px; transform-origin: 74.5px 8px; unicode-bidi: normal; "><span style="font-weight: 700; ">For 2 digits numbers:</span></span><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 283.5px 8px; transform-origin: 283.5px 8px; unicode-bidi: normal; "><span style=""> 11 and 17 are pair primes because both of them are 2 digits prime numbers and last digit of the first prime equals to the first digit of second prime number. 11 and 11 are not pair primes because a = b.</span></span></li><li style="block-size: 122.6px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 61.3px; text-align: left; transform-origin: 363px 61.3px; white-space: pre-wrap; margin-left: 56px; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 70.5px 8px; transform-origin: 70.5px 8px; unicode-bidi: normal; "><span style="font-weight: 700; ">For 3 digit numbers:</span></span><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 292px 8px; transform-origin: 292px 8px; unicode-bidi: normal; "><span style=""> 389 and 967 are pair primes because both of them are 3 digits prime numbers and last digit of the first prime equals to the first digit of the second prime number (797 and 797 are not pair primes because a = b). 467 and 673 are pair primes too because the last two digits of the first prime number (67) equals to the first two digit (67) of the second prime number. 211 and 113 are pair primes too but they satisfy two conditions: last digit of the first prime equals to the first digit of the second prime also last two digits of the first prime equals to the first two digits of the first prime.</span></span></li><li style="block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; "><span style="block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 70.5px 8px; transform-origin: 70.5px 8px; unicode-bidi: normal; "><span style="font-weight: 700; ">For 4 digit numbers:</span></span></li></ul><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: 244.5px 8px; transform-origin: 244.5px 8px; unicode-bidi: normal; "><span style="">1-) 1637 and 7549 are pair primes. First ends with 7 and second starts with 7.</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: 252px 8px; transform-origin: 252px 8px; unicode-bidi: normal; "><span style="">2-) 6221 and 2113 are pair primes. First ends with 21 and second starts with 21.</span></span></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: 383px 8px; transform-origin: 383px 8px; unicode-bidi: normal; "><span style="">3-) 1429 and 4297 are pair primes. First ends with 429 and second starts with 429. You should be careful. 2111 and 1117 are also four digit pair primes. It satisfies three conditions. First ends with 1 and second starts with 1. First ends with 11 and second starts with 11. First ends with 111 and second starts with 111. [2111 1117] pair should be counted for once.</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: 279px 8px; transform-origin: 279px 8px; unicode-bidi: normal; "><span style="">Given the digit counts, can you determine how many unique pair primes are there (a~=b)</span></span></div></div></div>

Let's define pair primes as follow;
For 2 digits numbers: 11 and 17 are pair primes because both of them are 2 digits prime numbers and last digit of the first prime equals to the first digit of second prime number. 11 and 11 are not pair primes because a = b.
For 3 digit numbers: 389 and 967 are pair primes because both of them are 3 digits prime numbers and last digit of the first prime equals to the first digit of the second prime number (797 and 797 are not pair primes because a = b). 467 and 673 are pair primes too because the last two digits of the first prime number (67) equals to the first two digit (67) of the second prime number. 211 and 113 are pair primes too but they satisfy two conditions: last digit of the first prime equals to the first digit of the second prime also last two digits of the first prime equals to the first two digits of the first prime.
For 4 digit numbers:
1-) 1637 and 7549 are pair primes. First ends with 7 and second starts with 7.
2-) 6221 and 2113 are pair primes. First ends with 21 and second starts with 21.
3-) 1429 and 4297 are pair primes. First ends with 429 and second starts with 429. You should be careful. 2111 and 1117 are also four digit pair primes. It satisfies three conditions. First ends with 1 and second starts with 1. First ends with 11 and second starts with 11. First ends with 111 and second starts with 111. [2111 1117] pair should be counted for once.
Given the digit counts, can you determine how many unique pair primes are there (a~=b)

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Last Solution submitted on Mar 20, 2023

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Alfonso Nieto-Castanon on 20 Oct 2017

there are quite a few look-up table solutions, could you perhaps add something like the following to the test suite to discourage these? assert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[51,2485,136162,8578934]),regexp(fileread('pairPrimes.m'),'[\d\.\+\-\*\/]+','match'))))

Peng Liu on 24 Oct 2017

Do you consider (13, 31) and (31, 13) as the same or different pair primes? Similarly, how about (79, 97) and (97, 79)?

Mehmet OZC on 24 Oct 2017

Thanks for pointing it out. They are different pair primes.

Rafael S.T. Vieira on 9 Jul 2020

Good problem. At first, I thought we needed to reverse the numbers, but only their order is necessary. And we need to count twice numbers like 31 and 13.

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