Perfect numbers: Difference between revisions

Line 1,294:

<lang perl>use ntheory qw/divisor_sum/;

sub is_perfect { my $n = shift; divisor_sum($n) == 2*$n; }</lang>

Use this naive method to show the first 5. Takes about 30 seconds ~~(half the time Pari/GP takes with this method)~~:

Use this naive method to show the first 5. Takes about 15 seconds:

<lang perl>use ntheory qw/divisor_sum/;

for (1..33550336) {

print "$_\n" if divisor_sum($_) == 2*$_;

}</lang>

Or we can be clever and look for 2^(p-1) * (2^p-1) where 2^p -1 is prime. The first 17 ~~are~~ ~~found~~ ~~in ~1~~ second~~, with the first 20 taking a bit under 10 seconds~~.

Or we can be clever and look for 2^(p-1) * (2^p-1) where 2^p -1 is prime. The first 20 takes about a second.

<lang perl>use ntheory qw/forprimes is_prime/;

use bigint;

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... 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423 ...

</pre>

We can speed this up even more using a faster program for printing the large results, as well as a faster primality solution. The first 38 in about 1 second with most of the time printing the large results. Caveat: this goes well past the current bound for odd perfect numbers and does not check for them.

<lang perl>use ntheory qw/forprimes is_mersenne_prime/;

use Math::GMP qw/:constant/;

forprimes {

print "$_\t", (2**$_-1)*2**($_-1),"\n" if is_mersenne_prime($_);

} 7_000_000;</lang>

=={{header|Perl 6}}==