1193 is 'rotationally prime' because 1193 and all of it's rotations (1931, 9311, and 3119) are prime. There is another set of 4-digit, and two sets of 5-digit rot-prime numbers. I think that's cool, but I'm not sure why...

Update: changed stop criteria in sub primelist from test/2 to sqrt(test). Thanks to larsen.

Also, there are two sets of 6 digit rot-prime numbers.

YuckFoo 

#!/usr/bin/perl

   use strict;

   my ($DIGITS) = (5);

   my ($list, $item);

   $list = primelist(10**$DIGITS);
   $list = rotatelist($list);

   for $item (@{$list}) { print "$item\n"; }

#-----------------------------------------------------------
sub rotatelist {

   my ($primes) = @_;
   my (@list, %phash, $prime, $sum);
   my ($rotations, $rotation);

   @phash{@{$primes}} = (1) x @{$primes};

   for $prime (@{$primes}) {

      $rotations = rotations($prime);

      if ($prime == $rotations->[0]) {

         $sum = 0;
         for $rotation (@{$rotations}) {
            $sum += $phash{$rotation};
         }

         if ($sum == @{$rotations}) { push (@list, $prime); }
      }
   }

   return \@list;
}

#-----------------------------------------------------------
sub rotations {

   my ($num) = @_;
   my (@list, @digs, $i);
   
   @digs = split('', $num);
   
   for ($i = 0; $i < length($num); $i++) {
      push (@digs, shift(@digs));
      push (@list, join ('', @digs) + 0);
   }
   
   @list = sort(@list);
   return \@list;
}

#-----------------------------------------------------------
sub primelist {
   
   my ($max) = @_;
   my ($test, $stop, $isprime, $prime);
   
   my (@primes) = qw(2);
   
   for ($test = 3; $test < $max; $test++) {
      
      $stop = sqrt($test);
      
      $isprime = 1;
      
      for $prime (@primes) {
         
         if ($prime > $stop) { last; }
         
         if ($test % $prime == 0) {
            $isprime = 0;
            last;
         }
      }
      
      if ($isprime) { push (@primes, $test); }
   }
   
   return \@primes;
}

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In reply to Rotationally Prime Numbers by YuckFoo

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