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 101 David Åkesson 11 49.7343 102 Charles Jackson 20 49.7195 103 Jan Kožíšek 13 49.6859 104 Bob Calvin 12 49.6855 105 Hans Joachim Böhm 16 49.6619 106 HyeongShin Kang 12 49.6372 107 Will Steinbach 10 49.6322 108 LeRoy Blanchard 11 49.5724 109 Per Provencher 7 49.5637 110 Greg Miller 7 49.5597 111 Jochen Beck 11 49.5585 112 Ralf Terber 20 49.5011 113 Philipp Bliedung 3 49.4832 114 Sascha Beat Dinkel 10 49.4830 115 Christian Wallbaum 11 49.4770 116 Ivy F. Tennant 17 49.4616 117 Igor Karpenko 1 49.4585 118 Gary Barnes 41 49.4530 119 Jordan Romaidis 6 49.4237 120 Oliver Kruse 14.8333 49.4053

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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)).