Proof-code: x25
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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 x25, one of those codes.

Code name (*):x25   (See the descriptive data below.)
Persons (*):2 (counting humans only)
Projects (*):0 (counting projects only)
Display (HTML):Water, Broadhurst, Primo, OpenPFGW
Number of primes:total 309
Unverified Primes:0 (prime table entries marked 'Composite','Untested', or 'InProcess')
Score for Primes (*):total 40.0848, on current list 39.6488
Entrance Rank (*):mean 44480.55 (minimum 10499, maximum 64653)

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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 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.

Usually, the largest effort was expended on GMP-ECM. Factorization percentages for current top-20s 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*2^65523-1639)-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.

Below is additional information about this entry.
Display (text):Water, Broadhurst, Primo, OpenPFGW
Display (short):Water & Broadhurst
Database id:113 (do not use this database id, it is subject to change)
Proof program:unknown
Entry last modified:2017-09-23 00:20:19