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.
||George Woltman's Prime95
||Jean Penné's LLR
[special, plus, minus]
||Geoffrey Reynolds' srsieve
||Reynolds and Brazier's PSieve
||Yves Gallot's Proth.exe
[other, special, plus, minus, classical]
||George Woltman's PRP
||Mikael Klasson's Proth_sieve
||David Underbakke's AthGFNSieve
||Phil Carmody's 'K' sieves
||Paul Jobling's SoBSieve
||Shoichiro Yamada's geneferCUDA
||OpenPFGW (a.k.a. PrimeForm)
[other, sieve, prp, special, plus, minus, classical]
||David Underbakke's GenefX64
||Paul Jobling's NewPGen
||David Underbakke's TwinGen
||Geoffrey Reynolds' gcwsieve
||Mark Rodenkirch's MultiSieve.exe
||Yves Gallot's GeneFer
||Jim Fougeron's GFNSieve
||Mark Rodenkirch's FactorialPrimorial Sieves
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.