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 125543 Mihai Preda's GpuOwl [prp, special] 1 58.0015 93006 George Woltman's Prime95 [special] 47 57.7015 43504 Jean Penné's LLR [special, plus, minus] 4726 56.9417 17509 Geoffrey Reynolds' srsieve [sieve] 2143 56.0316 17003 Yves Gallot's GeneFer [prp, special] 2446 56.0022 16914 Anand Nair's GFNSvCUDA sieve [sieve] 2444 55.9970 16875 David Underbakke's AthGFNSieve [sieve] 2448 55.9947 9218 Pavel Atnashev's PRST [] 299 55.3900 6821 EMsieve [sieve] 99 55.0888 6805 LLR2 [other] 1264 55.0865 6486 Anand Nair's CycloSvCUDA sieve [sieve] 27 55.0385 6229 Yves Gallot's Cyclo [special] 34 54.9980 4098 Reynolds and Brazier's PSieve [sieve] 1657 54.5794 3255 Geoffrey Reynolds' gcwsieve [sieve] 54 54.3491 1687 MultiSieve/mtsieve [sieve] 36 53.6918 1554 Mikael Klasson's Proth_sieve [sieve] 9 53.6098 1551 Phil Carmody's 'K' sieves [sieve] 7 53.6078 1551 Paul Jobling's SoBSieve [sieve] 7 53.6078 954 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 537 53.1214 185 Paul Jobling's NewPGen [sieve] 376 51.4830

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.