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 215482 Mihai Preda's GpuOwl [prp, special] 1 58.0015 159647 George Woltman's Prime95 [special] 56 57.7016 69348 Jean Penné's LLR [special, plus, minus] 4627 56.8678 29703 Geoffrey Reynolds' srsieve [sieve] 2578 56.0199 23927 Yves Gallot's GeneFer [prp, special] 1941 55.8036 23927 Anand Nair's GFNSvCUDA sieve [sieve] 1939 55.8036 23910 David Underbakke's AthGFNSieve [sieve] 1947 55.8029 15410 Pavel Atnashev's PRST [] 341 55.3637 11395 EMsieve [sieve] 101 55.0618 10902 LLR2 [other] 1139 55.0176 10820 Anand Nair's CycloSvCUDA sieve [sieve] 39 55.0100 10375 Yves Gallot's Cyclo [special] 44 54.9681 6804 Reynolds and Brazier's PSieve [sieve] 1938 54.5461 5556 Geoffrey Reynolds' gcwsieve [sieve] 57 54.3435 2902 MultiSieve/mtsieve [sieve] 41 53.6939 2671 Mikael Klasson's Proth_sieve [sieve] 11 53.6109 2662 Phil Carmody's 'K' sieves [sieve] 7 53.6078 2662 Paul Jobling's SoBSieve [sieve] 7 53.6078 1338 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 565 52.9199 320 Yves Gallot's Proth.exe [other, special, plus, minus, classical] 48 51.4887

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.