Proof-code: L214

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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 L214, one of those codes.

Code name (*):L214   (See the descriptive data below.)
Persons (*):1 (counting humans only)
Projects (*):0 (counting projects only)
Display (HTML):Broadhurst, NewPGen, LLR
Number of primes:total 46
Unverified Primes:0 (prime table entries marked 'Composite','Untested', or 'InProcess'
Score for Primes (*):total 43.3939

Descriptive Data: (report abuse)
I agree with Jean Penne that LLR is totally reliable in detecting and proving primes of the form k*2^n-1 with k > 2^53, albeit without the speed-up of George Woltman's gwnums. This LLR prover's code resulted from a successful attempt to refute ill-informed hearsay in another place.

After 4 primes were obtained at k > 2^60, the production rate for k ~ 2^47 was tested by searching for primes of the form (2*k+137137137137137)*2^333333-1, with k in [0,5*10^6]. The Poisson mean for such a range is mu=30/log(2)=43.3 and the standard deviation is sigma=sqrt(mu)=6.6. In the event, 42 such primes were found.

Moreover, 44,283 LLR tests were repeated, at 333 kbits, each on a processor different from that in the first run, as a hardware test. Thanks to the avoidance of over-clocking, not a single conflicting residue was detected.

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Below is additional information about this entry.

Display (text):Broadhurst, NewPGen, LLR
Display (short):Broadhurst
Database id:1298 (do not use this database id, it is subject to change)
Proof program:LLR  
Entry last modified:2024-11-21 21:37:09
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