Eratosthenes was a clever chap!

use strict;
use warnings;

use Benchmark qw{ cmpthese };

use Test::More tests => 1;
is_deeply(
   [ primes( 10000 ) ],
   [ primes_jg( 10000 ) ],
   'same'
   );

cmpthese(
   -10,
   {
       ch => 'primes( 10000 )',
       jg => 'primes_jg( 10000 )',
   }
   );

sub primes_jg
{
    my $limit     = shift;
    my $sqrtLimit = sqrt $limit;
    
    my $sieve                = q{};
    vec( $sieve, 0, 1 )      = 1;
    vec( $sieve, 1, 1 )      = 1;
    vec( $sieve, $limit, 1 ) = 0;

    my @primes;
    my $reached = 1;
    while( $reached < $sqrtLimit )
    {
        my $prime = $reached + 1;
        ++ $prime while vec( $sieve, $prime, 1 );
    
        push @primes, $prime;
        my $fill = 2 * $prime;
        while( $fill <= $limit )
        {
            vec( $sieve, $fill, 1 ) = 1;
            $fill += $prime;
        }
        $reached = $prime;
    }
    
    foreach my $value ( $reached + 1 .. $limit )
    {
        push @primes, $value unless vec( $sieve, $value, 1 );
    }

    return @primes;
}

sub primes {
    my $n = shift;
    return if $n < 2;

    my @primes = (2);
    for my $i (3 .. $n) {
        my $sqrt = sqrt $i;
        my $notprime;
        for my $p (@primes) {
            last if $p > $sqrt;

            $notprime = 1, last if 0 == $i % $p;
        }
        push @primes, $i unless $notprime;
    }
    return @primes
}
[download]

1..1
ok 1 - same
     Rate   ch   jg
ch 71.0/s   -- -25%
jg 94.7/s  33%   --
[download]

I hope this is of interest.

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