Top program sorted by normalized score

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 286353 Mihai Preda's GpuOwl [prp, special] 1 58.0015 212120 George Woltman's Prime95 [special] 56 57.7014 77349 Jean Penné's LLR [special, plus, minus] 4718 56.6926 36349 Geoffrey Reynolds' srsieve [sieve] 2829 55.9374 18489 David Underbakke's AthGFNSieve [sieve] 1688 55.2615 18312 Anand Nair's GFNSvCUDA sieve [sieve] 1678 55.2518 18306 Yves Gallot's GeneFer [prp, special] 1679 55.2515 16944 Pavel Atnashev's PRST [] 244 55.1742 15116 EMsieve [sieve] 103 55.0600 14352 Anand Nair's CycloSvCUDA sieve [sieve] 41 55.0081 13761 Yves Gallot's Cyclo [special] 50 54.9661 12766 LLR2 [other] 1157 54.8911 8794 Reynolds and Brazier's PSieve [sieve] 2178 54.5183 5820 Geoffrey Reynolds' gcwsieve [sieve] 55 54.1055 3552 Mikael Klasson's Proth_sieve [sieve] 14 53.6119 3538 Phil Carmody's 'K' sieves [sieve] 7 53.6078 3538 Paul Jobling's SoBSieve [sieve] 7 53.6078 2027 MultiSieve/mtsieve [sieve] 35 53.0508 1494 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 574 52.7455 427 Yves Gallot's Proth.exe [other, special, plus, minus, classical] 51 51.4929

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.