Top persons 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 Ed Goforth 9 50.4105 42 Ronny Willig 113 50.4090 43 Yair Givoni 1 50.3617 44 Sai Yik Tang 14 50.3488 45 Cesare Marini 1 50.3029 46 Honza Cholt 30 50.1738 47 Erik Veit 19 50.1200 48 Michael Curtis 43 49.9956 49 Masashi Kumagai 1 49.9772 50 Andrew M Farrow 3 49.9606 51 Tim McArdle 1 49.9091 52 Peyton Hayslette 1 49.8982 53 James Winskill 3 49.8904 54 Dmitry Domanov 31 49.8807 55 David Metcalfe 115 49.8732 56 Derek Gordon 1 49.7454 57 Patrice Salah 1 49.7436 58 Tim Terry 22 49.6294 59 Vaughan Davies 64 49.5899 60 Michael Goetz 5 49.5418

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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)).