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 277676 Mihai Preda's GpuOwl [prp, special] 1 58.0015 205693 George Woltman's Prime95 [special] 56 57.7014 75753 Jean Penné's LLR [special, plus, minus] 4700 56.7025 35851 Geoffrey Reynolds' srsieve [sieve] 2789 55.9544 18612 David Underbakke's AthGFNSieve [sieve] 1744 55.2989 18489 Pavel Atnashev's PRST [] 279 55.2922 18441 Yves Gallot's GeneFer [prp, special] 1736 55.2896 18440 Anand Nair's GFNSvCUDA sieve [sieve] 1734 55.2896 14658 EMsieve [sieve] 103 55.0600 13917 Anand Nair's CycloSvCUDA sieve [sieve] 41 55.0081 13344 Yves Gallot's Cyclo [special] 50 54.9661 12459 LLR2 [other] 1127 54.8975 8592 Reynolds and Brazier's PSieve [sieve] 2122 54.5259 7152 Geoffrey Reynolds' gcwsieve [sieve] 55 54.3424 3480 MultiSieve/mtsieve [sieve] 37 53.6222 3445 Mikael Klasson's Proth_sieve [sieve] 14 53.6119 3431 Phil Carmody's 'K' sieves [sieve] 7 53.6078 3431 Paul Jobling's SoBSieve [sieve] 7 53.6078 1446 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 572 52.7441 414 Yves Gallot's Proth.exe [other, special, plus, minus, classical] 51 51.4929

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.