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Re^2: a close prime number

by gam3 (Curate)
on Feb 14, 2005 at 18:44 UTC ( #430884=note: print w/ replies, xml ) Need Help??


in reply to Re: a close prime number
in thread a close prime number

The speed of the is_prime function can be increase by about 140% by using the 2 4 trick used below.

sub is_prime { my %prime = map { $_ => 1 } (2, 3, 5, 7); my %not_prime; return sub { my $n = shift; return 1 if $prime{ $n }; return 0 if $n % 2 == 0 || $n % 3 == 0 || exists $not_prime{ $n }; my $last = int sqrt $n; for ( my $x = 5; $x <= $last ;) { return $not_prime{ $n } = 0 if $n % $x == 0; $x += 2; return $not_prime{ $n } = 0 if $n % $x == 0; $x += 4; } return $prime{ $n } = 1; }; }
This version skips all of the numbers that are divisable by 2 and 3. Not checking numbers divisable by 2 is obvious, but not checking numbers divisable by 3 is less so, but reduces the search space by 25%.


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Re^3: a close prime number
by RazorbladeBidet (Friar) on Feb 14, 2005 at 19:01 UTC
    I wonder if it's quicker to add the digits of the number when you're checking to see if it's divisible by three and seeing if that resultant sum is divisible by three.
      It's not.
      use Benchmark qw( cmpthese ); my $large_number = 3 * 1234647389; cmpthese( -1, { modulo => sub { $large_number % 3 == 0 }, divide => sub { my $v; $v += $_ for split //, $large_number; $v % +3 == 0}, }); -------- Rate divide modulo divide 30919/s -- -99% modulo 2120579/s 6759% --

      By a factor of 67 times faster. Or so ...

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        Darn - so !(faster in my head == faster in code) :)

        Thanks for the benchmarks, dragonchild.
Re^3: a close prime number
by Limbic~Region (Chancellor) on Feb 15, 2005 at 22:32 UTC
    gam3,
    I have added several improvements:
    • Cache is now persistent
    • Primeness is determined in C
    • The 2 4 trick is used in checking near numbers also
    • An iterator is used in lieu of a stack

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