use Math::BigFloat;
use strict;
use warnings;

Math::BigFloat->accuracy(400);

# the length of the prime to find in e
my $prime_length = $ARGV[0] || 10;

# build e (1/0! + 1/1! + 1/2! + 1/3! + ... + 1/125!)
my $e = do {
  my $t = Math::BigFloat->new;
  $t += 1/Math::BigFloat->new($_)->bfac for 0..125;
  $t->bstr
};

# grab substrings
for (0 .. length($e) - $prime_length) {
  my $potential = substr $e, $_, $prime_length;
  print "found prime $potential \@ position $_\n" and last
    if is_prime($potential);
}

sub is_prime {
  my ($p) = @_;
  $p % $_ == 0 and return for 2, 3 .. sqrt($p);  # 2, 3 .. sqrt($p) is my trick
  return 1;
}