carmichael_lambda+1_is_prime_cached.pl

#!/usr/bin/perl

# Generate new Carmichael numbers of the form n*p,
# where n is a Carmichael number and p = lambda(n)+1 is prime.

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 $carmichael_file = "cache/factors-carmichael.storable";
my $carmichael      = retrieve($carmichael_file);

my %table;

sub my_carmichael_lambda ($factors) {
    Math::Prime::Util::GMP::lcm(map { Math::Prime::Util::GMP::subint($_, 1) } @$factors);
}

my %seen;

foreach my $n (keys %$carmichael) {

    #length($n) > 100 or next;

    my @factors = split(' ', $carmichael->{$n});
    my $lambda  = my_carmichael_lambda(\@factors);
    my $p       = Math::Prime::Util::GMP::addint($lambda, 1);

    if (Math::Prime::Util::GMP::modint($n, $p) > 0 and is_prime($p)) {
        my $c = Math::Prime::Util::GMP::mulint($n, $p);
        if (not exists $carmichael->{$c}) {
            say $c;
        }
    }

    #~ next if ($lambda < 1e10);
    #~ next if ($lambda > ~0);
    #~ next if $seen{$lambda}++;

    #~ say $lambda;
}