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- #!/usr/bin/perl
- # Thomas Ordowski asked:
- # Are there composite numbers n such that 2^n - 1 has all prime divisors p == 1 (mod n) ?
- # If both 2^p - 1 and 2^q - 1 are prime and n = pq is pseudoprime, then n is such a number.
- # However, the known Mersenne primes do not give such pseudoprimes.
- # http://list.seqfan.eu/pipermail/seqfan/2018-October/018943.html
- use 5.020;
- use strict;
- use warnings;
- use Storable;
- use Math::GMPz;
- use ntheory qw(:all);
- use Math::Prime::Util::GMP;
- use experimental qw(signatures);
- my $storable_file = "cache/factors-fermat.storable";
- my $numbers = retrieve($storable_file);
- while (my ($n, $value) = each %$numbers) {
- my @f = split(' ', $value);
- if (vecall { Math::Prime::Util::GMP::modint($_, $n) eq '1' } @f) {
- say $n;
- }
- }
- __END__
- # No such number is currently known.
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