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- #!/usr/bin/perl
- # Daniel "Trizen" Șuteu
- # Date: 17 March 2023
- # https://github.com/trizen
- # Generate Carmichael numbers from a given multiple.
- # See also:
- # https://trizenx.blogspot.com/2020/08/pseudoprimes-construction-methods-and.html
- use 5.036;
- use Math::GMPz;
- use ntheory qw(:all);
- sub carmichael_from_multiple ($m, $callback, $reps = 1e4) {
- my $t = Math::GMPz::Rmpz_init();
- my $u = Math::GMPz::Rmpz_init();
- my $v = Math::GMPz::Rmpz_init();
- is_square_free($m) || return;
- my $L = lcm(map { subint($_, 1) } factor($m));
- $m = Math::GMPz->new("$m");
- $L = Math::GMPz->new("$L");
- Math::GMPz::Rmpz_invert($v, $m, $L) || return;
- for (my $p = Math::GMPz::Rmpz_init_set($v) ; --$reps >= 0 ; Math::GMPz::Rmpz_add($p, $p, $L)) {
- Math::GMPz::Rmpz_gcd($t, $m, $p);
- Math::GMPz::Rmpz_cmp_ui($t, 1) == 0 or next;
- my @factors = factor_exp($p);
- (vecall { $_->[1] == 1 } @factors) || next;
- Math::GMPz::Rmpz_mul($v, $m, $p);
- Math::GMPz::Rmpz_sub_ui($u, $v, 1);
- Math::GMPz::Rmpz_set_str($t, lcm(map { subint($_->[0], 1) } @factors), 10);
- if (Math::GMPz::Rmpz_divisible_p($u, $t)) {
- $callback->(Math::GMPz::Rmpz_init_set($v));
- }
- }
- }
- my @list = (vecprod(5, 7, 13, 17, 19, 23));
- while (@list) {
- my $m = shift(@list);
- carmichael_from_multiple(
- $m,
- sub ($n) {
- say $n;
- push @list, $n;
- }
- );
- }
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