in reply to
Rotationally Prime Numbers

i wrote an algorithm to save you many, many cycles.

createPrimeVec() creates a bit vector of length $max. the value is 0 if prime, 1 otherwise. it uses the sieve of erathosthenes method to create the list. merlyn wrote a column on this some time ago (suprise!)

isprime() is a simple bit vector lookup, very fast.

rotPrime() cleverly appends the return value of chop to the beginning of the string.

here it is:

`#!/usr/local/bin/perl -w
use strict;
$|=1;
my $vecPrime;
my %rotPrime;
# allows specification of a range, such as (1000, 9999)
my ($min, $max) = (2, 999_999);
print "---creating prime vector (length: $max)\n";
$vecPrime = createPrimeVec($max);
print "---created\n\n";
print "---trying rotations $min..$max\n";
for($min..$max) {
next unless isprime($_);
my $x = rotPrime($_);
$x && $rotPrime{$x}++;
}
print "---tried $min..$max\n\n";
print "$_\n" for(sort {$a <=> $b} keys %rotPrime);
#----------
# return list of prime numbers up to and including value passed (defau
+lt:1000)
sub createPrimeVec {
my $UPPER = shift || 1000;
my $sieve = "";
GUESS: for (my $guess = 2; $guess <= $UPPER; $guess++) {
next GUESS if vec($sieve,$guess,1);
for(my $mults = $guess * $guess; $mults <= $UPPER; $mults += $
+guess) {
vec($sieve,$mults,1) = 1;
} }
return $sieve;
};
# returns true if found in prime number bit vector
sub isprime { return 1 if( vec($vecPrime,shift,1) == 0 ); };
# return smallest 'rotationally prime' number in set
# for instance, 1931, 9311, 3119, or 1193 yeilds return value 1193
sub rotPrime {
my ($num, $lchr, @list) = (shift);
for(1..length $num) {
$lchr = chop $num;
$num = $lchr . $num;
push @list, $num;
return unless isprime($num);
}
return (sort @list)[0];
};
`

i had used the prime number code for a program using fermat's factoring algorithm. perhaps i'll post it, assuming there's not a module to do that already.

~Particle