Top program sorted by number of primes

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.

rank program primes score 1 Jean Penné's LLR [special, plus, minus] 4652 56.7421 2 Geoffrey Reynolds' srsieve [sieve] 2660 56.0138 3 Reynolds and Brazier's PSieve [sieve] 1995 54.5416 4 David Underbakke's AthGFNSieve [sieve] 1877 55.3859 5 Yves Gallot's GeneFer [prp, special] 1870 55.3870 6 Anand Nair's GFNSvCUDA sieve [sieve] 1868 55.3869 7 LLR2 [other] 1114 55.0061 8 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 569 52.9050 9 Paul Jobling's NewPGen [sieve] 380 51.4547 10 Pavel Atnashev's PRST [] 335 55.3548 11 Marcel Martin's Primo [general] 318 46.6639 12 CM a fast ECPP implementation Andreas Enge [general] 122 42.1812 13 EMsieve [sieve] 101 55.0599 14 Robert Gerbicz's PolySieve [sieve] 63 48.8311 15 Geoffrey Reynolds' gcwsieve [sieve] 58 54.3437 16 George Woltman's Prime95 [special] 55 57.7014 17 Yves Gallot's Proth.exe [other, special, plus, minus, classical] 49 51.4896 18 Yves Gallot's Cyclo [special] 44 54.9659 19 MultiSieve/mtsieve [sieve] 41 53.6939 20 Anand Nair's CycloSvCUDA sieve [sieve] 39 55.0080

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.<\p>