Top programs sorted by Number of primes
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
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The Prover-Account Top 20
Persons by: number score normalized score
Programs by: number score normalized score
Projects by: number score normalized score

At this site we keep several lists of primes, most notably the list of the 5,000 largest known primes. Who found the most of these record primes? We keep separate counts for persons, projects and programs. To see these lists click on 'number' to the right.

Clearly one 100,000,000 digit prime is much harder to discover than quite a few 100,000 digit primes. Based on the usual estimates we score the top persons, provers and projects by adding ‎(log n)3 log log n‎ for each of their primes n. Click on 'score' to see these lists.

Finally, to make sense of the score values, we normalize them by dividing by the current score of the 5000th prime. See these by clicking on 'normalized score' in the table on the right.

rankprogramprimesscore
1 Jean Penné's LLR [special, plus, minus] 4879 53.5048
2 Geoffrey Reynolds' srsieve [sieve] 3119 53.2560
3 Reynolds and Brazier's PSieve [sieve] 2757 52.5974
4 David Underbakke's TwinGen [sieve] 1608 51.0947
5 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 550 50.8553
6 Marcel Martin's Primo (was Titanix and Certifix) [general] 373 42.8312
7 Paul Jobling's NewPGen [sieve] 298 50.0187
8 Yves Gallot's Proth.exe [other, special, plus, minus, classical] 131 51.5023
9 George Woltman's PRP [prp] 61 51.4655
10 Geoffrey Reynolds' gcwsieve [sieve] 39 49.8691
11 David Underbakke's AthGFNSieve [sieve] 37 51.4318
12 Dubner Cruncher [other, prp, plus, minus, classical] 29 34.3273
12 John Renze's Coppersmith-Howgrave-Graham PARI script [classical] 29 43.7484
14 Mikael Klasson's Proth_sieve [sieve] 27 51.4459
15 Mark Rodenkirch's MultiSieve.exe [sieve] 24 49.6723
16 George Woltman's Prime95 [special] 19 56.3333
17 EMsieve [sieve] 18 48.8716
18 Yves Gallot's GeneFer [prp, special] 15 46.7003
19 Phil Carmody's 'K' sieves [sieve] 13 51.3970
20 Jim Fougeron's GFNSieve [sieve] 8 45.9060
20 Mark Rodenkirch's FactorialPrimorial Sieves [sieve] 8 46.5559
 
 

Notes:

The list above show the programs that are used the most (either by number or score). In some ways this is useless because we are often comparing apples and oranges, that is why the comments in brackets attempt to say what each program does. See the help page for some explanation of these vague categories

Number of primes

When counting primes we decided that if three people (persons) went together to find a prime, each should get credit for 1/3 of a prime. The same is true for projects, however programs get full credit for each prime (to encourage honest reporting of what programs where used). Persons, programs and projects are three separate categories and do not compete against each other.

For example, suppose the persons 'Carmody' and 'Caldwell' worked together and used the program 'PRP' to test candidates selected by the 'GFN 2^13 Sieving project', then completed their proofs using 'Proth.exe'. Then the persons 'Carmody' and 'Caldwell' would get 1/2 credit for each prime found; but the project 'GFN 2^13 Sieving project' and the programs 'PRP' and 'Proth.exe' would each get full credit.