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- #!/usr/bin/perl
- # Daniel "Trizen" Șuteu
- # License: GPLv3
- # Date: 20 September 2016
- # Website: https://github.com/trizen
- # A very fast function that returns true when a given number is even-perfect. False otherwise.
- # See also:
- # https://en.wikipedia.org/wiki/Perfect_number
- use 5.010;
- use strict;
- use warnings;
- use Math::AnyNum qw(:overload is_power isqrt);
- use ntheory qw(is_mersenne_prime is_prime_power);
- sub is_even_perfect {
- my ($n) = @_;
- $n % 2 == 0 || return 0;
- my $square = 8 * $n + 1;
- is_power($square, 2) || return 0;
- my $tp = (isqrt($square) + 1) / 2;
- my $k = is_prime_power($tp, \my $base) || return 0;
- defined($base) && ($base == 2) && is_mersenne_prime($k) ? 1 : 0;
- }
- say is_even_perfect(191561942608236107294793378084303638130997321548169216); # true
- say is_even_perfect(191561942608236107294793378084303638130997321548169214); # false
- say is_even_perfect(191561942608236107294793378084303638130997321548169218); # false
- say is_even_perfect(14474011154664524427946373126085988481573677491474835889066354349131199152128); # true
- # A much larger perfect number
- say is_even_perfect(Math::AnyNum->new('141053783706712069063207958086063189881486743514715667838838675999954867742652380114104193329037690251561950568709829327164087724366370087116731268159313652487450652439805877296207297446723295166658228846926807786652870188920867879451478364569313922060370695064736073572378695176473055266826253284886383715072974324463835300053138429460296575143368065570759537328128'));
- # Search test
- say "=> Perfect numbers below 10^4:";
- for my $n (1 .. 10000) {
- is_even_perfect($n) && say $n;
- }
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