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 259211 Mihai Preda's GpuOwl [prp, special] 1 58.0015 192015 George Woltman's Prime95 [special] 56 57.7014 71208 Jean Penné's LLR [special, plus, minus] 4661 56.7095 33911 Geoffrey Reynolds' srsieve [sieve] 2718 55.9676 17874 David Underbakke's AthGFNSieve [sieve] 1814 55.3272 17719 Pavel Atnashev's PRST [] 318 55.3185 17714 Yves Gallot's GeneFer [prp, special] 1806 55.3182 17714 Anand Nair's GFNSvCUDA sieve [sieve] 1804 55.3182 13682 EMsieve [sieve] 102 55.0599 12990 Anand Nair's CycloSvCUDA sieve [sieve] 40 55.0081 12456 Yves Gallot's Cyclo [special] 47 54.9660 11695 LLR2 [other] 1092 54.9030 8032 Reynolds and Brazier's PSieve [sieve] 2045 54.5273 6681 Geoffrey Reynolds' gcwsieve [sieve] 56 54.3431 3255 MultiSieve/mtsieve [sieve] 40 53.6242 3215 Mikael Klasson's Proth_sieve [sieve] 13 53.6116 3203 Phil Carmody's 'K' sieves [sieve] 7 53.6078 3203 Paul Jobling's SoBSieve [sieve] 7 53.6078 1353 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 571 52.7465 386 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.