experimental-projects/pseudoprimes/programs/extra-strong_lucas_not_lucas.pl

#!/usr/bin/perl

# Find extra-strong Lucas pseudoprimes that are not regular Lucas pseudoprimes.

# The first few terms are:
#   989, 3239, 27971, 29681, 30739, 31631, 125249, 137549, 137801, 153931

# See also:
#   https://oeis.org/A217120 -- Lucas pseudoprimes
#   https://oeis.org/A217719 -- Extra strong Lucas pseudoprimes

use 5.020;
use strict;
use warnings;

use Math::Prime::Util::GMP qw(
  is_pseudoprime
  is_lucas_pseudoprime
  is_extra_strong_lucas_pseudoprime
  is_almost_extra_strong_lucas_pseudoprime
);

my %seen;

while (<>) {
    next if /^\h*#/;
    /\S/ or next;
    my $n = (split(' ', $_))[-1];

    $n || next;

    next if ($n < ~0);

    #next if length($n) > 40;

    is_pseudoprime($n, 2) && next;
    is_lucas_pseudoprime($n) && next;

    if (   is_extra_strong_lucas_pseudoprime($n)
        || is_almost_extra_strong_lucas_pseudoprime($n)) {
        say $n if !$seen{$n}++;
    }
}

__END__
# Some examples greater than 2^64:

21979710862205324399
31155533865320225759
32614974548912586599
46675503329187754391
47137357874632210499
68891633072323569191
110010529523011784831
181792908157826671439
187961990407258205591
204775845664488874991
206459139977493134399
206560670024345256791
206675382180674432759
294453521939438917439
298428222066624344999
336947701713570561239
513398368200012052799
557700139349287019399
798909849426402491399

# Some examples with more than 3 factors:

1441047407316299
757833929289202499
27292658179482499859
76400587170813605849
137534203921819545569
299651357354898181499
635873639357398391459
688263201326737424489
849911100465285007379
850047981592775523011
903938650523935653059
2319023344998942960299
2510072121079439620259
39383652460474120698899
84512947066721812244219
233535954319253909204699
432509954733989656647779
4904416886890491872853899
3039165753384639348162300649999