Re: Rotationally Prime Numbers

[particle]

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

[YuckFoo]

Thanks particle,

Great improvement. I purposefully didn't use the sieve method for memory considerations, but I see this is an ideal situation for vec. Something I've been aware of, but never really found a use for.

YuckFoo

[thinker]

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.

Surely there was space in the margin to post it :-)