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, Primo, OpenPFGW, Unknown
Number of primes: total 15
Unverified Primes: 0 (prime table entries marked 'Composite','Untested', or 'InProcess')
Score for Primes ( *): total 39.4560, on current list 39.4560
Entrance Rank ( *): mean 57761.87 (minimum 48943, maximum 66967)
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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) Pari-GP and Primo (when needed) for proving these
(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.
Below is additional information about this entry.
Display (text): Batalov, Primo, OpenPFGW, 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: 2019-10-23 01:20:14