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 109108 Mihai Preda's GpuOwl [prp, special] 1 58.0015 80828 George Woltman's Prime95 [special] 45 57.7015 38759 Jean Penné's LLR [special, plus, minus] 4708 56.9665 15900 Geoffrey Reynolds' srsieve [sieve] 2079 56.0755 15702 Yves Gallot's GeneFer [prp, special] 2519 56.0630 15625 Anand Nair's GFNSvCUDA sieve [sieve] 2517 56.0580 15591 David Underbakke's AthGFNSieve [sieve] 2521 56.0558 8697 Pavel Atnashev's PRST [] 324 55.4721 5993 LLR2 [other] 1238 55.0998 5928 EMsieve [sieve] 104 55.0888 5637 Anand Nair's CycloSvCUDA sieve [sieve] 27 55.0385 5413 Yves Gallot's Cyclo [special] 34 54.9980 3679 Reynolds and Brazier's PSieve [sieve] 1613 54.6119 2828 Geoffrey Reynolds' gcwsieve [sieve] 53 54.3487 1464 MultiSieve/mtsieve [sieve] 34 53.6904 1351 Mikael Klasson's Proth_sieve [sieve] 9 53.6098 1348 Phil Carmody's 'K' sieves [sieve] 7 53.6078 1348 Paul Jobling's SoBSieve [sieve] 7 53.6078 819 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 520 53.1099 165 Paul Jobling's NewPGen [sieve] 376 51.5076

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.