Proof-code: L4561

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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 L4561, one of those codes.

Code name (*):L4561   (See the descriptive data below.)
Persons (*):2 (counting humans only)
Projects (*):1 (counting projects only)
Display (HTML):Propper, Batalov, CycloSv, Cyclo, EMsieve, PIES, LLR
Number of primes:total 7
Unverified Primes:0 (prime table entries marked 'Composite','Untested', or 'InProcess'
Score for Primes (*):total 54.9631, on current list 54.9631 (normalized score 13399)
Entrance Rank (*):mean 275.14 (minimum 7, maximum 477)

Descriptive Data: (report abuse)
P.I.E.S. is the decade-old project to search for primes of the form Φm(b) where m is a 3-smooth number.

Yves Gallot's Cyclo program (both CPU and GPU implementations) can be used for m = 3 * 2n. Prime95 with the option PhiExtensions=1 (or LLR with modifications) can be used for m = 3v * 2n, where v<=2; for v=1, this is 1.25-1.5x slower than CycloCPU but the range of values of b is 1.5x wider.
In addition, Prime95 (and LLR ver. >= 3.8.19) can be run in multi-threaded mode, so the double-check can be an order of magnitude faster than the intitial test.

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Below is additional information about this entry.

Display (text):Propper, Batalov, CycloSv, Cyclo, EMsieve, PIES, LLR
Display (short):Propper & Batalov
Database id:8426 (do not use this database id, it is subject to change)
Proof program:LLR  The primes from this code accounts for 0.149% of the (active) primes and 17.588% of the (active) score for this program.
Entry last modified:2025-05-12 12:37:09
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