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 390124 Mihai Preda's GpuOwl [prp, special] 1 58.0015 288994 George Woltman's Prime95 [special] 59 57.7014 98647 Jean Penné's LLR [special, plus, minus] 4721 56.6266 47766 Geoffrey Reynolds' srsieve [sieve] 3132 55.9013 21511 Pavel Atnashev's PRST [] 220 55.1036 20596 EMsieve [sieve] 77 55.0601 19553 Anand Nair's CycloSvCUDA sieve [sieve] 41 55.0081 18919 David Underbakke's AthGFNSieve [sieve] 1344 54.9752 18749 Yves Gallot's Cyclo [special] 51 54.9662 18677 Anand Nair's GFNSvCUDA sieve [sieve] 1334 54.9623 18670 Yves Gallot's GeneFer [prp, special] 1335 54.9620 16465 LLR2 [other] 1088 54.8363 11672 Reynolds and Brazier's PSieve [sieve] 2399 54.4922 7937 Geoffrey Reynolds' gcwsieve [sieve] 62 54.1065 4842 Mikael Klasson's Proth_sieve [sieve] 16 53.6124 4820 Phil Carmody's 'K' sieves [sieve] 7 53.6078 4820 Paul Jobling's SoBSieve [sieve] 7 53.6078 2456 MultiSieve/mtsieve [sieve] 35 52.9336 1949 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 413 52.7022 575 Yves Gallot's Proth.exe [other, special, plus, minus, classical] 55 51.4814

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.