#! /usr/bin/perl -w
use strict;

print "$_\n" for 2, 3, 5, 7;
my @d = (1, 3, 7, 9);
my %seen;
for my $length (2..(shift || 6)) {
  # print "Length: $length\n";
  LIMIT: for my $limit (0..3) {
    my @indexes = $limit - 1;
    NUMBER: while (1) {
      $indexes[-1]++;
      while ($indexes[-1] > $limit) {
        pop @indexes;
        next LIMIT unless @indexes;
        $indexes[-1]++;
      }
      while (@indexes < $length) {
        push @indexes, 0;
      }
      my $num = join '', @d[@indexes];
      for (1..$length) {
        next NUMBER unless is_prime_for_odds_over_3($num);
        $num =~ s/(\d)(\d*)/$2$1/;
      }
      for (1..$length) {
        print "$num\n" unless $seen{$num}++;
        $num =~ s/(\d)(\d*)/$2$1/;
      }
    }
  }
}


sub is_prime_for_odds_over_3 {
  my $n = shift;
  my $max = sqrt($n);
  return 0 unless $n % 3;
  my $div = 5;
  while ($div <= $max) {
    return 0 unless $n % $div;
    $div += 2;
    return 0 unless $n % $div;
    $div += 4;
  }
  return 1;
}
[download]

It's already very fast, but you can improve it somewhat by doing your rotations with

$num = chop($num) . $num;



      Rate    s chop
s    258/s   -- -14%
chop 299/s  16%   --
[download]

the lowliest monk

tilly,
I certainly considered this approach in theory. I just couldn't see an easy way to jump and that's the real trick. Without the jump, then you end up incrementing/testing far too much. I love looking at a problem in a new light - Thanks!

Cheers - L~R