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 114353 Mihai Preda's GpuOwl [prp, special] 1 58.0015 84715 George Woltman's Prime95 [special] 46 57.7015 39971 Jean Penné's LLR [special, plus, minus] 4720 56.9504 16652 Geoffrey Reynolds' srsieve [sieve] 2106 56.0748 15799 Yves Gallot's GeneFer [prp, special] 2496 56.0222 15718 Anand Nair's GFNSvCUDA sieve [sieve] 2494 56.0170 15683 David Underbakke's AthGFNSieve [sieve] 2498 56.0148 9064 Pavel Atnashev's PRST [] 313 55.4665 6266 LLR2 [other] 1252 55.0974 6213 EMsieve [sieve] 104 55.0888 5908 Anand Nair's CycloSvCUDA sieve [sieve] 27 55.0385 5673 Yves Gallot's Cyclo [special] 34 54.9980 3794 Reynolds and Brazier's PSieve [sieve] 1619 54.5956 2964 Geoffrey Reynolds' gcwsieve [sieve] 53 54.3487 1536 MultiSieve/mtsieve [sieve] 35 53.6911 1416 Mikael Klasson's Proth_sieve [sieve] 9 53.6098 1413 Phil Carmody's 'K' sieves [sieve] 7 53.6078 1413 Paul Jobling's SoBSieve [sieve] 7 53.6078 862 OpenPFGW (a.k.a. PrimeForm) [other, sieve, prp, special, plus, minus, classical] 523 53.1134 173 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.