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 308548 George Woltman's Prime95 [special] 58 57.7012 102773 Jean Penné's LLR [special, plus, minus] 4762 56.6019 43290 Geoffrey Reynolds' srsieve [sieve] 3169 55.7373 21985 EMsieve [sieve] 82 55.0597 20885 Anand Nair's CycloSvCUDA sieve [sieve] 46 55.0084 20022 Yves Gallot's Cyclo [special] 51 54.9662 19552 David Underbakke's AthGFNSieve [sieve] 1294 54.9424 19294 Anand Nair's GFNSvCUDA sieve [sieve] 1284 54.9291 19286 Yves Gallot's GeneFer [prp, special] 1285 54.9288 15648 LLR2 [other] 1079 54.7197 15378 Pavel Atnashev's PRST [] 168 54.7023 12155 Reynolds and Brazier's PSieve [sieve] 2442 54.4671 7102 Geoffrey Reynolds' gcwsieve [sieve] 58 53.9297 5172 Mikael Klasson's Proth_sieve [sieve] 17 53.6126 5147 Phil Carmody's 'K' sieves [sieve] 7 53.6078 5147 Paul Jobling's SoBSieve [sieve] 7 53.6078 2194 MultiSieve/mtsieve [sieve] 33 52.7551 1639 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 411 52.4635 615 Yves Gallot's Proth.exe [other, special, plus, minus, classical] 56 51.4830 604 George Woltman's PRP [prp] 28 51.4657

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.