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 41 Ken Glennie 2 50.6508 42 Honza Cholt 25 50.5779 43 Michael Schulz 1 50.5434 44 Peter Benson 44 50.5202 45 Ed Goforth 7 50.5142 46 Karsten Klopffleisch 1 50.5009 47 Roman Vogt 3 50.4948 48 Barry Schnur 4 50.4782 49 Max Dettweiler 65 50.4641 50 Florian Piesker 111 50.4597 51 Serhiy Gushchak 1 50.4356 52 Peter Harvey 3 50.4233 53 Borys Jaworski 15 50.4207 54 Michael Millerick 13 50.4163 55 Marius Vultur 19 50.4054 56 Seonghwan Kim 43 50.3675 57 Yair Givoni 1 50.3617 58 James Krauss 9 50.3521 59 Sai Yik Tang 10 50.3491 60 Cesare Marini 1 50.3029

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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)).