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 118639 Mihai Preda's GpuOwl [prp, special] 1 58.0015 87890 George Woltman's Prime95 [special] 46 57.7015 41266 Jean Penné's LLR [special, plus, minus] 4721 56.9454 17135 Geoffrey Reynolds' srsieve [sieve] 2123 56.0665 16207 Yves Gallot's GeneFer [prp, special] 2473 56.0109 16123 Anand Nair's GFNSvCUDA sieve [sieve] 2471 56.0057 16086 David Underbakke's AthGFNSieve [sieve] 2475 56.0034 9282 Pavel Atnashev's PRST [] 308 55.4535 6465 LLR2 [other] 1259 55.0918 6445 EMsieve [sieve] 104 55.0888 6129 Anand Nair's CycloSvCUDA sieve [sieve] 27 55.0385 5886 Yves Gallot's Cyclo [special] 34 54.9980 3889 Reynolds and Brazier's PSieve [sieve] 1632 54.5835 3075 Geoffrey Reynolds' gcwsieve [sieve] 53 54.3487 1594 MultiSieve/mtsieve [sieve] 36 53.6918 1469 Mikael Klasson's Proth_sieve [sieve] 9 53.6098 1466 Phil Carmody's 'K' sieves [sieve] 7 53.6078 1466 Paul Jobling's SoBSieve [sieve] 7 53.6078 897 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 526 53.1168 180 Paul Jobling's NewPGen [sieve] 377 51.5114

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.