DouKaku?

use strict;
use warnings;
use Math::Prime::XS qw(is_prime);
use List::Util qw(reduce);
use List::MoreUtils qw(pairwise);

sub primes {
    my $number = shift;
    my @primes = (2);
    my $i      = 3;
    while ( @primes < $number ) {
        push( @primes, $i ) if is_prime($i);
        $i++;
    }
    return @primes;
}

sub goedel {
    my $number = shift;
    my @num    = split //, $number;
    my @primes = primes( scalar(@num) );
    reduce { $a * $b } pairwise { $a**$b } @primes, @num;
}

print goedel(9);
print goedel(81);
print goedel(230);