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 132810 Mihai Preda's GpuOwl [prp, special] 1 58.0015 98389 George Woltman's Prime95 [special] 47 57.7015 45547 Jean Penné's LLR [special, plus, minus] 4713 56.9313 18474 Geoffrey Reynolds' srsieve [sieve] 2178 56.0290 17543 Yves Gallot's GeneFer [prp, special] 2406 55.9772 17449 Anand Nair's GFNSvCUDA sieve [sieve] 2404 55.9719 17407 David Underbakke's AthGFNSieve [sieve] 2408 55.9695 9711 Pavel Atnashev's PRST [] 306 55.3858 7215 EMsieve [sieve] 99 55.0888 7150 LLR2 [other] 1268 55.0797 6862 Anand Nair's CycloSvCUDA sieve [sieve] 27 55.0385 6589 Yves Gallot's Cyclo [special] 34 54.9980 4311 Reynolds and Brazier's PSieve [sieve] 1685 54.5738 3424 Geoffrey Reynolds' gcwsieve [sieve] 54 54.3433 1786 MultiSieve/mtsieve [sieve] 37 53.6923 1644 Mikael Klasson's Proth_sieve [sieve] 9 53.6098 1641 Phil Carmody's 'K' sieves [sieve] 7 53.6078 1641 Paul Jobling's SoBSieve [sieve] 7 53.6078 1009 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 537 53.1213 193 Paul Jobling's NewPGen [sieve] 376 51.4699

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.