why aren't you eliminating the numbers which end with 2, 4, 5, 6, 8, and 0 before doing any math

If you want you can, but how do you spot those numbers? you are using a regex that, as you can guess, is slower than math checks. Theese numbers will be catched with the modulo operator anyway, as choroba explained.
Also the regex in the original code is also not correct: you skip 2 and 5. 
perl -e "map {print qq($_ ) unless $_ =~/(2|4|5|6|8|0)$/ } @ARGV" 2 3 
+5 7 11 13 17 19 23 29 37
3 7 11 13 17 19 23 29 37

[download]
i used a different regex (and precompiled in the bench program using qr'\d[245680]$'): 
perl -e "map {print qq($_ ) unless $_ =~/\d[245680]$/ } @ARGV" 2 3 5 7
+ 11 13 17 19 23 29 37
2 3 5 7 11 13 17 19 23 29 37

[download]
About saving time skipping numbers ending with some fixed digit, as said, the regex solution is slower: with this code: 

use strict;
use warnings;

use Benchmark qw{ cmpthese };

my $skipper_regex = qr'\d[245680]$';

sub primes_original {
    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
}

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

    my @primes = (2);
    for my $i (3 .. $n) {
        next if $i =~ $skipper_regex;
        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
}

##

sub primes_opt_till_11 {
    my $n = shift;
    return if $n < 2;

    my @primes = (2);
    for my $i (3 .. $n) {
                if($i > 2 || $i % 2 == 0){next}
                if($i > 3 || $i % 3 == 0){next}
                if($i > 5 || $i % 5 == 0){next}
                if($i > 7 || $i % 7 == 0){next}
                if($i > 11 || $i % 11 == 0){next}

        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
}
##
use Test::More tests => 1;
is_deeply([primes_original(10000)], [primes_skipper(10000)], "same");

cmpthese(-10,
        {
primes_original => 'primes_original (10000)',
primes_skipper  => 'primes_skipper  (10000)',
primes_opt_till_11  => 'primes_opt_till_11  (10000)',
 });

[download]
You will see a significant decreese of speed if you skip numbers using a regex: 
1..1
ok 1 - same
                     Rate    primes_skipper   primes_original primes_o
+pt_till_11
primes_skipper     33.5/s                --              -35%         
+      -94%
primes_original    51.4/s               53%                --         
+      -90%
primes_opt_till_11  519/s             1448%              909%         
+        --

[download]

HtH
L*
There are no rules, there are no thumbs..
Reinvent the wheel, then learn The Wheel; may be one day you reinvent one of THE WHEELS.

In reply to Re^8: Number functions.. primes (ugly code runs faster) by Discipulus
in thread Number functions I have lying around by Lady_Aleena

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