Re^2: Number functions I have lying around

[Discipulus]

And you can profit of an enhencemt if you too add if($i%2==0){next} before eleborating the square root, as you can see in the ch_opt row.

          Rate     la     di     ch ch_opt
la     0.329/s     --   -99%   -99%   -99%
di      25.3/s  7600%     --   -50%   -56%
ch      50.4/s 15230%    99%     --   -12%
ch_opt  57.6/s 17417%   127%    14%     --

L*

[Anonymous Monk]

A modest improvement in speed may be obtained if one implements the wheel.

For example (the modulus is relatively cheap in perl):

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

    my @primes = (2);

I:  for my $i (3 .. $n) {
        next unless 0x208a28aa & (1 << $i % 30);

        my $sqrt = int sqrt $i;
        for my $p (@primes) {
            next I unless $i % $p;
            last if $p > $sqrt;
        }
        push @primes, $i;
    }
    return @primes
}

[Anonymous Monk]

Actually, it's 0x208a2882, but you have to initialize primes to (2, 3, 5) then..