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 and ggnfs for extracting PrP factors of such cyclotomic cofactors.

(3) Primo and VFYPR for proving these helpers prime.

(4) OpenPFGW for BLS tests with these prime helpers.

(5) Pari-GP for 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.