Recently for a project I started, I needed to find prime numbers. I'm not particularly worried about large prime numbers, but if someone asks for them, this module can be really slow. With caching, it speeds up quite a bit, but can still be slow the first time it hits a large number.

package Math::Name::To::Be::Determined;

use warnings;
use strict;

our $VERSION = '0.01';

use vars qw(@ISA @EXPORT_OK %EXPORT_TAGS);
use Exporter;
@ISA = 'Exporter';

@EXPORT_OK = qw(
  clear_prime_cache
  is_prime
  primes_upto
);

%EXPORT_TAGS = (
    all => \@EXPORT_OK,
);

{
    my ( @PRIMES, %IS_PRIME );
    clear_prime_cache();

    sub is_prime {
        my $number = shift;
        return 1 if $IS_PRIME{$number};
        return   if $number < $PRIMES[-1];

        my $is_prime;
        for ( $PRIMES[-1] + 1 .. $number ) {

            # cache prime numbers
            if ( $is_prime = _is_prime($_) ) {
                push @PRIMES => $_;
            }
        }
        return $is_prime;
    }

    sub _is_prime {
        my $number = shift;
        return unless _is_integer($number);
        return 1 if $IS_PRIME{$number};
        return unless $number > 2 and $number % 2;

        my $max = 1 + int $number**.5;
        for ( my $divisor = 3; $divisor < $max; $divisor += 2 ) {
            return unless $number % $divisor;
        }
        $IS_PRIME{$number} = 1;    # cache it
        return 1;
    }

    sub primes_upto {
        my $number = shift;
        if ( $number > $PRIMES[-1] ) {

            # extend cache
            is_prime($number);
        }

        my (@primes);
        foreach my $i ( 0 .. @PRIMES ) {
            next if $number > $PRIMES[$i];
            @primes = @PRIMES[ 0 .. $i - 1 ] if $i;
            last;
        }
        return wantarray ? @primes : \@primes;
    }

    sub clear_prime_cache {
        @PRIMES = _get_primes();
        %IS_PRIME = map { $_ => 1 } @PRIMES;
        return;
    }
}

sub _is_integer {
    return shift =~ /^[-+]?\d+$/;
}

sub _get_primes {

    # list from Crypt::Primes
    # http://search.cpan.org/dist/Crypt-Primes/
    return (
        # huge list of all primes < 2^16
    );
}

1;
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This is part of a larger set of code which is intended to be pure Perl, but given that I'm not a mathematician, I'm not sure if this is the best approach. I make heavy use of caching and my tests pass, but I'm wondering if there is not a better approach to writing both &is_prime and &primes_upto. Even with heavy caching, finding primes significantly larger than 2^16 can be pretty slow.