...
my @list = (20, 48, 96, 7, 69, 33, 13195,  600851475143, 2147483647, 18, 54, 27000, 29474100, 589806);
foreach my $n ( @list ) {
    my @result = prime_factors($n);
    print "Number: $n , Prime_Factors: => @result", "\n";
}

use Benchmark qw(cmpthese);
cmpthese( -10, {
    once =>  sub { prime_factors($_)        for @list },
    every => sub { prime_factors_sqrt($_)   for @list },
});
__END__
...
        Rate  once every
once  16.9/s    --  -94%
every  286/s 1593%    --