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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 Limbic~Region (Chancellor) on Feb 15, 2005 at 22:32 UTC
gam3,
• 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
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 ...

Being right, does not endow the right to be rude; politeness costs nothing.
Being unknowing, is not the same as being stupid.
Expressing a contrary opinion, whether to the individual or the group, is more often a sign of deeper thought than of cantankerous belligerence.
Do not mistake your goals as the only goals; your opinion as the only opinion; your confidence as correctness. Saying you know better is not the same as explaining you know better.

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

Thanks for the benchmarks, dragonchild.

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