{
    my %prime_cache;
    my $max_checked;
    BEGIN {
        $prime_cache{2} = undef;
        $max_checked = 2;
    }

    sub is_prime {
        my ($to_check) = @_;

        sieve_up_to($to_check);
        return exists $prime_cache{$to_check};
    }

    sub sieve_up_to {
        my ($to_check) = @_;

        while ( $max_checked < $to_check ) {
            sieve_part($to_check);
        }
    }

    sub sieve_part {
        my ($to_check) = @_;

        $to_check++ if !($to_check % 2);
        my $max_this_part = $to_check;
        if ( ($max_checked * $max_checked) < $to_check ) {
            $max_this_part = $max_checked * $max_checked;
        }

        my %to_sieve = map { $_ => undef } ($max_checked + 1 .. $max_this_part);
        for my $prime (keys %prime_cache) {
            my $base = $max_checked - ($max_checked % $prime) + $prime;
            while ( $base <= $max_this_part ) {
                delete $to_sieve{$base};
                $base += $prime;
            }
        }

        while ( my $new_prime = each %to_sieve ) {
            $prime_cache{$new_prime} = undef;
        }

        $max_checked = $max_this_part;
    }
}