Proof-code: CH3

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 CH3, one of those codes.

Code name (*):CH3   (See the descriptive data below.)
Persons (*):2 (counting humans only)
Projects (*):0 (counting projects only)
Display (HTML):Broadhurst, Water, OpenPFGW, Primo, CHG
Number of primes:total 31
Unverified Primes:0 (prime table entries marked 'Composite','Untested', or 'InProcess'
Score for Primes (*):total 37.5328, on current list 36.7200
Entrance Rank (*):mean 23265.20 (minimum 17766, maximum 31920)

Descriptive Data: (report abuse)
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 for proving these helpers prime.

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

(5) David Broadhurst's corrections to John Renze's implementation of CHG in Pari-GP for exhausting the residue classes established by PFGW.

The largest effort was expended on GMP-ECM. Factorization percentages for some current top-20s are listed at this yahoo page, in the cases primV and lucasU, and here, in the case of Lehmer numbers.

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Below is additional information about this entry.

Display (text):Broadhurst, Water, OpenPFGW, Primo, CHG
Display (short):Broadhurst & Water
Database id:1073 (do not use this database id, it is subject to change)
Proof program:CHG  The primes from this code accounts for 17.241% of the (active) primes and 0.001% of the (active) score for this program.
Entry last modified:2024-06-22 03:37:35
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