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] 4199 50.9423 2 Geoffrey Reynolds' srsieve [sieve] 2935 50.2765 3 Paul Jobling's NewPGen [sieve] 1100 49.7447 4 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 793 48.5505 5 Yves Gallot's Proth.exe [other, special, plus, minus, classical] 507 51.4701 6 Marcel Martin's Primo (was Titanix and Certifix) [general] 315 39.4546 7 George Woltman's PRP [prp] 311 51.4716 8 David Underbakke's TwinGen [sieve] 203 46.9008 9 Phil Carmody's Phi Sieves [sieve] 160 46.6993 9 Phil Carmody's ForEis [prp, special] 160 46.6993 11 Jim Fougeron's FermFact program [sieve] 142 45.9970 12 Mikael Klasson's Proth_sieve [sieve] 93 51.4510 13 Phil Carmody's 'K' sieves [sieve] 73 51.3991 14 Dubner Cruncher [other, prp, plus, minus, classical] 47 43.2733 15 Mark Rodenkirch's MultiSieve.exe [sieve] 41 49.5293 16 John Renze's Coppersmith-Howgrave-Graham PARI script [classical] 30 38.3835 17 Jim Fougeron's GFNSieve [sieve] 19 46.0518 17 Geoffrey Reynolds' gcwsieve [sieve] 19 49.5136 19 David Underbakke's AthGFNSieve [sieve] 18 47.5940 20 Jens Kruse Andersen's APTreeSieve [sieve] 16 33.1426

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.