The following will speed up your calculation significantly:

# Doing $x ** $y can result in very large numbers,
# But if what you want it ( $x ** $y ) % $m, then
# you can pull the modulo into the products and keep
# your numbers smaller.
sub ModuloPwr
{
    my($base,$pwr,$mod) = @_;
    return 1 if $pwr < 1;
    # I probably don't need the 0.1, but doesn't hurt.
    my $result =  ModuloPwr($base, int(0.1 + $pwr/2), $mod);
    $result = ($result * $result) % $mod;
    if ($pwr%2) {
        $result = ( $result * $base ) % $mod;
    }
    return $result;
}
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However there appears to be a bug somewhere. It works fine for small primes, but for instance 97397 is reported not a prime, while it is. (I checked and double-checked. My change does not cause the issue.)

UPDATE
I am a moron. The bug is simple and obvious. Square then reduce modulo the prime works fine until the prime is large enough to go outside of native integer arithmetic. At that point things go haywire.