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 6

Unverified Primes: 1 (prime table entries marked 'Composite','Untested', or 'InProcess'

Score for Primes (*): total 54.2994, on current list 54.2994 (normalized score 13220)

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 Φ_m(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 = 3^v * 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 0.122% of the (active) primes and 11.704% of the (active) score for this program.

Entry last modified: 2023-10-04 18:37:18

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 6
Unverified Primes:	1 (prime table entries marked 'Composite','Untested', or 'InProcess'
Score for Primes (*):	total 54.2994, on current list 54.2994 (normalized score 13220)
Entrance Rank (*):	mean 275.14 (minimum 7, maximum 477)

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 0.122% of the (active) primes and 11.704% of the (active) score for this program.
Entry last modified:	2023-10-04 18:37:18