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] 4723 56.9358 2 David Underbakke's AthGFNSieve [sieve] 2431 55.9808 3 Yves Gallot's GeneFer [prp, special] 2429 55.9884 4 Anand Nair's GFNSvCUDA sieve [sieve] 2427 55.9831 5 Geoffrey Reynolds' srsieve [sieve] 2154 56.0288 6 Reynolds and Brazier's PSieve [sieve] 1667 54.5744 7 LLR2 [other] 1266 55.0821 8 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 538 53.1224 9 Paul Jobling's NewPGen [sieve] 375 51.4646 10 Marcel Martin's Primo [general] 309 46.6639 11 Pavel Atnashev's PRST [] 294 55.3846 12 CM a fast ECPP implementation Andreas Enge [general] 146 42.4265 13 EMsieve [sieve] 99 55.0888 14 Robert Gerbicz's PolySieve [sieve] 66 48.8311 15 Geoffrey Reynolds' gcwsieve [sieve] 54 54.3433 16 George Woltman's Prime95 [special] 47 57.7015 17 Yves Gallot's Proth.exe [other, special, plus, minus, classical] 38 51.4485 17 David Underbakke's TwinGen [sieve] 38 48.3645 17 MultiSieve/mtsieve [sieve] 38 53.6929 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>