Sexy Primes are pairs of numbers \$(n, n+6)\$ such as \$n\$ and \$n+6\$ are both prime

You need to create a function which will take an integer, check for sexy primes from 0 to that integer, and return an array of arrays.

For example, listSexy(30) must return [[5,11], [7,13], [11,17], [13,19], [17,23], [23,29]] or some equivalent.

This is so the program with the shortest bytecount wins!

  • \$\begingroup\$ Can you explain what the desired output format looks like? \$\endgroup\$ – Howard Jun 26 '12 at 14:34
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    \$\begingroup\$ Bah, I hate it when the challenge changes after answers have been submitted. \$\endgroup\$ – Griffin Jun 26 '12 at 15:25
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    \$\begingroup\$ Is there a certain reason to check from 0? Why shouldn't I check from (5,11)? A short definition of sexy primes should be given right here, while linking to Wikipedia for further reading is welcome. \$\endgroup\$ – user unknown Jun 27 '12 at 14:45
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    \$\begingroup\$ In Portuguese Sexy Primes translates to the same as Sexy Cousins! \$\endgroup\$ – sergiol Nov 6 '17 at 23:35
  • \$\begingroup\$ @sergiol haha... \$\endgroup\$ – Victor VosMottor Jul 28 '20 at 10:50

34 Answers 34


PHP, 106 bytes

function p($n){for($i=$n;--$i&&$n%$i;);return$i-1;}for(;++$i<$argv[1]-5;)p($i)|p($k=$i+6)?:print"$i,$k\n";

program prints pairs as n,n+6 delimited by linebreaks. Run with -r.

I modified my is_prime function (& saved a byte) so that it returns 0 for primes to golf on the Elvis.


CJam, 27 bytes


It prints pairs as two lines with one number each on then, largest to smallest. See the TIO for the example from the question.

Try it online


ri                              input an integer
  )                             increment
   ,{                    }%     iterate "m" from 0 to n-1
     __                         create two copies
       6+                       add 6
         _                      copy
          mp                    check if m+6 is prime
            @                   rotate so m is on top
             mp                 check if m is prime
               &                bitwise AND on two prime checks
                        ?       ternary if-else
                {pp}            if primes, print top two numbers
                    {;;}        otherwise, discard them

JavaScript (V8), 104 bytes


Try it online!


Excel, 131 bytes


Link to Spreadsheet


  • =LET( allows defined names within formulas.
  • x,SEQUENCE(A1), x = 1..A1 listed vertically.
  • y,TRANSPOSE(x), y = 1..A1 listed horizontally.
  • (MOD(x,y)=0)*1 creates a matrix this is 1 if x mod y = 0 and 0 otherwise.
  • MMULT(~,x^0) sums the elements of each row with matrix multiplication. x^0 is a vertical matrix of 1s.
  • z,x*(~=2), if the sum = 2 then x is prime and z=x else z=0.
  • ,a,IFERROR(INDEX(z,x+{0,6}),), creates an array a where the first column is z and the second is z offset by 6 rows.
  • FILTER(a,MMULT(SIGN(a),{1;1})=2) returns the rows of a that have no zeros.

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