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- #!/usr/bin/perl
- # Daniel "Trizen" Șuteu
- # License: GPLv3
- # Date: 17 June 2017
- # https://github.com/trizen
- # Prime product, related to the zeta function.
- # ___
- # | | (p^(2n) - 1) / (p^(2n) + 1) = {2/5, 6/7, 691/715, 7234/7293, 523833/524875, ...}
- # p
- # Example:
- # Product_{n >= 1} (prime(n)^2 - 1)/(prime(n)^2 + 1) = 2/5
- use 5.010;
- use strict;
- use warnings;
- use ntheory qw(forprimes);
- my $n = 2;
- {
- my $prod = 1;
- forprimes {
- $prod *= ($_**$n + 1) / ($_**$n - 1);
- } 1e7;
- say $prod;
- }
- {
- my $prod = 1;
- forprimes {
- $prod *= ($_**$n + 1) / ($_**$n - 1);
- } 1e8;
- say $prod;
- say 1 / $prod;
- }
- __END__
- 2.49999997066443
- 2.49999999690776
- 0.400000000494758
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