Proof-code: x45

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Samuel Yates began, and this site continues, a database of the largest known primes. Primes in that database are assigned a proof-code to show who should be credited with the discovery as well as what programs and projects they used. (Discoverers have one prover-entry, but may have many proof-codes because they use a variety of programs...)

This page provides data on x45, one of those codes.

Code name (*):x45   (See the descriptive data below.)
Persons (*):1 (counting humans only)
Projects (*):0 (counting projects only)
Display (HTML):Batalov, OpenPFGW, Primo, Unknown
Number of primes:total 18
Unverified Primes:0 (prime table entries marked 'Composite','Untested', or 'InProcess'
Score for Primes (*):total 42.9727, on current list 42.9725
Entrance Rank (*):mean 56037.06 (minimum 23322, maximum 65043)

Descriptive Data: (report abuse)
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) Pari-GP and Primo (when needed) 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.
Ref: https://web.archive.org/web/20170120062023/http://physics.open.ac.uk/~dbroadhu/cert/kppm.gp

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Below is additional information about this entry.

Display (text):Batalov, OpenPFGW, Primo, Unknown
Display (short):Batalov
Database id:8789 (do not use this database id, it is subject to change)
Proof program:(see the descriptive data above)
Entry last modified:2025-09-30 14:37:10
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