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 246902 Mihai Preda's GpuOwl [prp, special] 1 58.0015 182896 George Woltman's Prime95 [special] 56 57.7014 69739 Jean Penné's LLR [special, plus, minus] 4653 56.7373 33611 Geoffrey Reynolds' srsieve [sieve] 2669 56.0074 17770 David Underbakke's AthGFNSieve [sieve] 1858 55.3700 17617 Yves Gallot's GeneFer [prp, special] 1850 55.3614 17617 Anand Nair's GFNSvCUDA sieve [sieve] 1848 55.3614 17329 Pavel Atnashev's PRST [] 321 55.3449 13031 EMsieve [sieve] 101 55.0599 12372 Anand Nair's CycloSvCUDA sieve [sieve] 39 55.0080 12265 LLR2 [other] 1095 54.9993 11863 Yves Gallot's Cyclo [special] 44 54.9659 7706 Reynolds and Brazier's PSieve [sieve] 2003 54.5346 6364 Geoffrey Reynolds' gcwsieve [sieve] 56 54.3431 3325 MultiSieve/mtsieve [sieve] 41 53.6939 3061 Mikael Klasson's Proth_sieve [sieve] 12 53.6113 3050 Phil Carmody's 'K' sieves [sieve] 7 53.6078 3050 Paul Jobling's SoBSieve [sieve] 7 53.6078 1513 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 571 52.9068 367 Yves Gallot's Proth.exe [other, special, plus, minus, classical] 50 51.4903

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.