Proof-code: x18

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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 x18, one of those codes.

Code name (*):x18   (See the descriptive data below.)
Persons (*):2 (counting humans only)
Projects (*):0 (counting projects only)
Display (HTML):Irvine, Broadhurst
Number of primes:total 4
Unverified Primes:0 (prime table entries marked 'Composite','Untested', or 'InProcess'
Score for Primes (*):total 33.2392

Descriptive Data: (report abuse)
This code is used for proofs of generalized repunits and Lucas numbers. The following software was used: (1) Pari-GP for cyclotomic (and, where appropriate, Aurifeuillian) factorizations of N^2-1. (2) GMP-ECM and MPQS 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. The distinctive contribution of Sean Irvine was to provide factorizations by massively parallel use of MPQS.
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Below is additional information about this entry.

Display (text):Irvine, Broadhurst
Display (short):Irvine & Broadhurst
Database id:490 (do not use this database id, it is subject to change)
Proof program:unknown
Entry last modified:2024-04-20 02:37:14
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