This code is used for proofs of generalized Lucas and
Lehmer numbers and their primitive parts.
The following software was used:
(1) PariGP for cyclotomic (and, where appropriate,
Aurifeuillian) factorizations of N^21.
(2) GMPECM, Msieve, YAFU and ggnfs for extracting PrP
factors of such cyclotomic cofactors.
(3) PariGP and Primo (when needed) for proving these
helpers prime.
(4) OpenPFGW for BLS tests with these prime helpers.
(5) PariGP for CoppersmithHowgraveGraham,
WilliamsLenstra, or KonyaginPomerance proofs, where
BLS was insufficient.
Usually, the largest effort was expended on GMPECM.
Factorization percentages for current top20s are listed
here,
in the cases primV and lucasU, and here,
in the case of Lehmer numbers and their primitive parts.
PS: We also included:
6738*(2^148227+60443)*(205*2^655231639)1, with a
KonyaginPomerance proof that depends on the
cyclotomy of 2^655201;
two gigantic generalized repunits, with BLS proofs
involving ECPP helpers at 3832
and 4354
digits.
