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 4102225 George Woltman's Prime95 [special] 13 55.8432 51814 George Woltman's PRP [prp] 311 51.4716 51734 Yves Gallot's Proth.exe [other, special, plus, minus, classical] 507 51.4701 50756 Mikael Klasson's Proth_sieve [sieve] 93 51.4510 48192 Phil Carmody's 'K' sieves [sieve] 73 51.3991 47892 Paul Jobling's SoBSieve [sieve] 6 51.3929 30523 Jean Penné's LLR [special, plus, minus] 4199 50.9424 15684 Geoffrey Reynolds' srsieve [sieve] 2934 50.2766 9214 Paul Jobling's NewPGen [sieve] 1100 49.7447 7429 Mark Rodenkirch's MultiSieve.exe [sieve] 41 49.5293 7313 Geoffrey Reynolds' gcwsieve [sieve] 19 49.5136 2791 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 793 48.5505 1073 David Underbakke's AthGFNSieve [sieve] 18 47.5940 539 David Underbakke's TwinGen [sieve] 204 46.9063 438 Phil Carmody's Phi Sieves [sieve] 160 46.6993 438 Phil Carmody's ForEis [prp, special] 160 46.6993 229 Jim Fougeron's GFNSieve [sieve] 19 46.0518 217 Jim Fougeron's FermFact program [sieve] 142 45.9970 158 David Underbakkes GenefX64 [special] 1 45.6772 31 3 P's Suite [special] 10 44.0595

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.