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] 4719 56.9454 2 David Underbakke's AthGFNSieve [sieve] 2477 56.0036 3 Yves Gallot's GeneFer [prp, special] 2475 56.0111 4 Anand Nair's GFNSvCUDA sieve [sieve] 2473 56.0059 5 Geoffrey Reynolds' srsieve [sieve] 2119 56.0663 6 Reynolds and Brazier's PSieve [sieve] 1629 54.5827 7 LLR2 [other] 1258 55.0917 8 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 525 53.1157 9 Paul Jobling's NewPGen [sieve] 377 51.5114 10 Pavel Atnashev's PRST [] 308 55.4535 11 Marcel Martin's Primo [general] 298 46.6639 12 CM a fast ECPP implementation Andreas Enge [general] 157 42.4472 13 EMsieve [sieve] 104 55.0888 14 Robert Gerbicz's PolySieve [sieve] 66 48.8311 15 Geoffrey Reynolds' gcwsieve [sieve] 53 54.3487 16 George Woltman's Prime95 [special] 46 57.7015 17 David Underbakke's TwinGen [sieve] 39 48.5275 18 Yves Gallot's Proth.exe [other, special, plus, minus, classical] 38 51.4485 19 MultiSieve/mtsieve [sieve] 36 53.6918 20 Yves Gallot's Cyclo [special] 34 54.9980

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>