For larger numbers, say: 66_666_666_666_666_666_666_666_666_666_666_666_666_667 you can use use some tricks that will proves that a number is composite. Here is a script that gives a better that 50% chance that a number is prime. By looping you can reduce the chance that a number is that not prime is reported as prome. 10 loops gives a 1 in 2^10 chance of being wrong.

#!/usr/bin/perl

use strict;

use Math::BigInt::GMP;

# Precondition: a, n >= 0; n is odd
use strict;
use warnings;
#use diagnostics;

use Crypt::OpenSSL::Random;
use Data::Dumper;
use Math::BigInt;
use Math::BigFloat;

sub brand {
   my $number = shift;
   my $n = Math::BigInt->new($number);
   my $l = Math::BigFloat->new($n + 1)->blog(2)->bceil;
   my $r = 0;

   while ($r == 0 or $r >= $n) {
        my $x = Crypt::OpenSSL::Random::random_pseudo_bytes(10);
        $r = Math::BigInt->new('0b' . unpack("B$l", $x));
        if ($r < $n and $r) {
            last;
        } else {
#           printf "rand miss\n";
        }
    }
    return $r;
}


sub jacobi
{
  my ($a, $n) = @_;

die unless defined $a;

  if ($a == 0) {                # identity 1
    return ($n == 1) ? 1 : 0;
  }
  if ($a == 2) {                # identity 2
    my $x = $n % 8;
    if ($x == 1 || $x == 7) {
      return 1;
    } elsif ($x == 3 || $x == 5) {
      return -1;
    }
  }
  if ( $a >= $n ) {             # identity 3
    return jacobi($a % $n, $n);
  }
  if ($a % 2 == 0) {            # identity 4
    return jacobi(2, $n) * jacobi($a/2, $n);
  }
  die if $a % 2 == 0;
                                # identities 5 and 6
  return ($a % 4 == 3 && $n % 4 == 3) ? -jacobi($n, $a) : jacobi($n, $
+a);
}
sub check
{
    my $number = shift;

    my $n = Math::BigInt->new($number);

    return 'Composite 0' if $n->copy->bmod(2) == 0;

    my $a = 0;
    while ($a == 0) {
        $a = brand($number);
    }
    return 'Composite 1' if (1 != $a->copy->bgcd($n));

    my $x = ($n - 1) / 2;

    my $q =  $a->copy->bmodpow($x, $n);

#    die 'bad math' unless $q == $q_p;

    my $j = jacobi($a, $n);

    $j %= $n;

    if ($j == $q) {
        return 'Prime.';
    } else {
        return 'Composite 2';
    }
}

my $number = shift || die "Need a number.";
my $loops = shift || 10;

die if ($loops < 0);

my $c = 0;

while ($c++ < $loops) {
    my $ret = check($number);
    if ($ret =~ /Composite/) {
        print $ret, "\n";
        exit;
    }
}

print "This is only a 1/2^", $loops, " chance that $number is not prim
+e\n";
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