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 187164 Mihai Preda's GpuOwl [prp, special] 1 58.0015 138666 George Woltman's Prime95 [special] 55 57.7016 62288 Jean Penné's LLR [special, plus, minus] 4639 56.9013 25946 Geoffrey Reynolds' srsieve [sieve] 2496 56.0255 22765 Yves Gallot's GeneFer [prp, special] 2052 55.8947 22765 Anand Nair's GFNSvCUDA sieve [sieve] 2050 55.8947 22749 David Underbakke's AthGFNSieve [sieve] 2057 55.8940 13586 Pavel Atnashev's PRST [] 357 55.3786 10180 EMsieve [sieve] 99 55.0899 9681 Anand Nair's CycloSvCUDA sieve [sieve] 38 55.0397 9676 LLR2 [other] 1189 55.0392 9295 Yves Gallot's Cyclo [special] 43 54.9990 6000 Reynolds and Brazier's PSieve [sieve] 1884 54.5614 4824 Geoffrey Reynolds' gcwsieve [sieve] 55 54.3431 2518 MultiSieve/mtsieve [sieve] 38 53.6928 2320 Mikael Klasson's Proth_sieve [sieve] 11 53.6109 2312 Phil Carmody's 'K' sieves [sieve] 7 53.6078 2312 Paul Jobling's SoBSieve [sieve] 7 53.6078 1440 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 556 53.1342 275 Yves Gallot's Proth.exe [other, special, plus, minus, classical] 45 51.4788

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.