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] 4721 56.6266 2 Geoffrey Reynolds' srsieve [sieve] 3132 55.9013 3 Reynolds and Brazier's PSieve [sieve] 2399 54.4922 4 David Underbakke's AthGFNSieve [sieve] 1344 54.9752 5 Yves Gallot's GeneFer [prp, special] 1335 54.9620 6 Anand Nair's GFNSvCUDA sieve [sieve] 1334 54.9623 7 LLR2 [other] 1088 54.8363 8 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 413 52.7022 9 Marcel Martin's Primo [general] 284 46.6396 10 Paul Jobling's NewPGen [sieve] 252 51.4459 11 Pavel Atnashev's PRST [] 220 55.1036 12 CM a fast ECPP implementation Andreas Enge [general] 110 41.8789 13 EMsieve [sieve] 77 55.0601 14 Geoffrey Reynolds' gcwsieve [sieve] 62 54.1065 15 George Woltman's Prime95 [special] 59 57.7014 16 Yves Gallot's Proth.exe [other, special, plus, minus, classical] 55 51.4814 17 Robert Gerbicz's PolySieve [sieve] 53 48.8305 18 Yves Gallot's Cyclo [special] 51 54.9662 19 Anand Nair's CycloSvCUDA sieve [sieve] 41 55.0081 20 David Underbakke's TwinGen [sieve] 35 47.2653 20 MultiSieve/mtsieve [sieve] 35 52.9336

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>