Top programs 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] 4926 55.6791 2 Geoffrey Reynolds' srsieve [sieve] 3132 54.9418 3 Reynolds and Brazier's PSieve [sieve] 2389 53.9279 4 David Underbakke's AthGFNSieve [sieve] 1470 54.1127 5 Yves Gallot's GeneFer [prp, special] 1460 54.0438 6 Anand Nair's GFNSvCUDA sieve [sieve] 1459 54.0448 7 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 467 51.1327 8 Marcel Martin's Primo [general] 392 46.6400 9 Paul Jobling's NewPGen [sieve] 300 51.0359 10 LLR2 [other] 250 53.3100 11 Yves Gallot's Proth.exe [other, special, plus, minus, classical] 79 51.5010 12 EMsieve [sieve] 68 52.8094 13 Anand Nair's CycloSvCUDA sieve [sieve] 62 52.5376 14 George Woltman's Prime95 [special] 57 57.7002 15 George Woltman's PRP [prp] 47 51.4828 16 Geoffrey Reynolds' gcwsieve [sieve] 44 52.9846 17 Robert Gerbicz's PolySieve [sieve] 36 48.8303 18 Mark Rodenkirch's MultiSieve.exe [sieve] 35 52.3424 19 David Underbakke's TwinGen [sieve] 31 47.0272 20 Dubner Cruncher [other, prp, plus, minus, classical] 29 34.3273

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.