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This code is used for proofs of generalized Lucas and
Lehmer numbers and their primitive parts.
The following software was used:
(1) Pari-GP for cyclotomic (and, where appropriate,
Aurifeuillian) factorizations of N^2-1.
(2) GMP-ECM, Msieve, YAFU and ggnfs for extracting PrP
factors of such cyclotomic cofactors.
(3) Primo, Pari-GP and VFYPR for proving these helpers
prime.
(4) OpenPFGW for BLS tests with these prime helpers.
(5) Pari-GP for Coppersmith--Howgrave-Graham,
Williams--Lenstra, or Konyagin--Pomerance proofs, where BLS
was insufficient.
By far the largest effort was expended on GMP-ECM.
Factorization percentages for current top-20s are listed at
this yahoo page, in the cases primV and lucasU, and
here, in the case of Lehmer numbers.
PS: We also included:
6738*(2^148227+60443)*(205*2^65523-1639)-1, with a Konyagin-Pomerance
proof that depends on the cyclotomy of 2^65520-1;
two gigantic generalized repunits, with BLS proofs
involving ECPP helpers at 3832
and 4354
digits.
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