Top person sorted by 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.

rank person primes score 201 Scott Earle 3 49.0986 202 Dao Heng Liu 10 49.0798 203 Rafael Trigueiro 4 49.0735 204 Vladislav Ketamino 9 49.0564 205 Jonathan Gehrke 9 49.0019 206 Takeshi Nakamura 10 48.9994 207 Denis Iakovlev 1 48.9974 208 Patrick Schöfer 3 48.9968 209 Logan Hood 2 48.9964 210 Roman Strajt 10 48.9957 211 John S Chambers 3 48.9893 212 William Pomeranke 2 48.9834 213 Yifei Gao 8 48.9818 214 Michael Becker 7 48.9777 215 Ian Dickinson 9 48.9737 216 Sean Humphries 2 48.9729 217 Martin Vanc 1 48.9657 218 Steven Wong 9 48.9646 219 Norbert Schneider 2 48.9615 220 Johnathan Chu 8 48.9605

move up list ↑

move down list ↓

Notes:

Score for Primes

To find the score for a person, program or project's primes, we give each prime n the score (log n)³ log log n; and then find the sum of the scores of their primes. For persons (and for projects), if three go together to find the prime, each gets one-third of the score. Finally we take the log of the resulting sum to narrow the range of the resulting scores. (Throughout this page log is the natural logarithm.)

How did we settle on (log n)³ log log n? For most of the primes on the list the primality testing algorithms take roughly O(log(n)) steps where the steps each take a set number of multiplications. FFT multiplications take about

O( log n ^. log log n ^. log log log n )

operations. However, for practical purposes the O(log log log n) is a constant for this range number (it is the precision of numbers used during the FFT, 64 bits suffices for numbers under about 2,000,000 digits).

Next, by the prime number theorem, the number of integers we must test before finding a prime the size of n is O(log n) (only the constant is effected by prescreening using trial division).  So to get a rough estimate of the amount of time to find a prime the size of n, we just multiply these together and we get

O( (log n)³ log log n ).

Finally, for convenience when we add these scores, we take the log of the result.  This is because log n is roughly 2.3 times the number of digits in the prime n, so (log n)³ is quite large for many of the primes on the list. (The number of decimal digits in n is floor((log n)/(log 10)+1)).