Here is a script that implements the "Sieve of Eratosthenes" which is another way of finding primes. Eratosthenes was a Carthaginian mathematician living at around 250BC. I have used a vector but a list would work as well.

use strict;
use warnings;

my $limit = shift or die "No limit supplied\n";
die "Limit is not integer\n" unless $limit =~ /^\d+$/;
my $sqrtLimit = sqrt $limit;
my $sieve = "";
vec($sieve, 0, 1) = 1;
vec($sieve, 1, 1) = 1;
vec($sieve, $limit, 1) = 0;
my $reached = 1;
while($reached < $sqrtLimit)
{
    my $prime = $reached + 1;
    ++ $prime while vec($sieve, $prime, 1);
    print "$prime is a prime\n";
    my $fill = 2 * $prime;
    while($fill <= $limit)
    {
        vec($sieve, $fill, 1) = 1;
    $fill += $prime;
    }
    $reached = $prime;
}
foreach my $value ($reached + 1 .. $limit)
{
    print "$value is a prime\n" unless vec($sieve, $value, 1);
}

[download]

I hope this is of interest. It seems to run quite quickly.

Cheers,

JohnGG

Update: I've just realised I had posted this script before in here.

In reply to Re: Primes. Again. by johngg
in thread Primes. Again. by Andrew_Levenson

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