weak_lucas.pl

#!/usr/bin/perl

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

# The first few terms, are:
#   5459, 16109, 18971, 22499, 24569, 25199, 58519, 97439, 115639, 130139, 158399, 176399, 176471, 192509, 197801, 224369, 230691, 243629, 253259

# There are more than 136014 such terms below 2^64.

use 5.020;
use strict;
use warnings;

use ntheory qw(:all);
use Math::GMPz;

my %seen;

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

    $n || next;

    next if ($n < ~0);

    is_pseudoprime($n, 2) && next;
    is_strong_lucas_pseudoprime($n) || next;
    is_extra_strong_lucas_pseudoprime($n) && next;

    say $n if !$seen{$n}++;
}

__END__
Some examples greater than 2^64:

20408982770556851329
20568342387213435209
23670706525594498439
24847222806013007489
26086391151191854649
29068260741176977039
33151779267787421639
36870561701473163999
39984382030247659439
41323030592365869719
55315344601090493639
56054136269755951799
57727823262395133229
57877454423821667039
59219085813138083699
59481665238642827729
60741844475142237041
62233144753874792039
66935800363893170219
77429723166908158049
81737863165920691199
96850125428211990449