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.

normalized program primes score 741584 George Woltman's Prime95 [special] 23 56.3334 21348 Jean Penné's LLR [special, plus, minus] 4797 52.7855 14796 Geoffrey Reynolds' srsieve [sieve] 4036 52.4189 9686 Reynolds and Brazier's PSieve [sieve] 3551 51.9952 5771 Yves Gallot's Proth.exe [other, special, plus, minus, classical] 186 51.4774 5708 George Woltman's PRP [prp] 97 51.4665 5601 Mikael Klasson's Proth_sieve [sieve] 33 51.4476 5493 David Underbakke's AthGFNSieve [sieve] 31 51.4281 5316 Phil Carmody's 'K' sieves [sieve] 11 51.3954 5303 Paul Jobling's SoBSieve [sieve] 6 51.3929 3927 Shoichiro Yamada's geneferCUDA [] 7 51.0926 2387 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 516 50.5947 1439 David Underbakke's GenefX64 [special] 6 50.0884 1376 Paul Jobling's NewPGen [sieve] 426 50.0440 1207 David Underbakke's TwinGen [sieve] 520 49.9130 975 Geoffrey Reynolds' gcwsieve [sieve] 35 49.6994 914 Mark Rodenkirch's MultiSieve.exe [sieve] 27 49.6350 28 Yves Gallot's GeneFer [prp, special] 9 46.1652 22 Jim Fougeron's GFNSieve [sieve] 8 45.9060 20 Mark Rodenkirch's FactorialPrimorial Sieves [sieve] 5 45.8273

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

normalized score

Just how do you make sense out of something as vague as our 'score' for primes? One possibility is to compare the amount of effort involved in earning that score, with the effort required to find the 5000th prime on the list. The normalized score does this: it is the number of primes that are the size of the 5000th, required to earn the same score (rounded to the nearest integer).

Note that if a program stops finding primes, its normalized score will steadily drop as the size of the 5000th primes steadily increases. The non-normalized scores drop too, but not as quickly because they only drop when the program's primes are pushed off the list.