Top person sorted by score

The Prover-Account Top 20
Persons by: number score normalized score
Programs by: number score normalized score
Projects by: number score normalized 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.

21 Wolfgang Schwieger 79 51.8464
22 Marc Wiseler 12 51.8138
23 Diego Bertolotti 1 51.6397
24 Rudi Tapper 6 51.6228
25 Stefan Larsson 142 51.3783
26 Brian D. Niegocki 41 51.3370
27 Randall Scalise 148 51.2334
28 Peter Kaiser 84.3333 51.0046
29 Hiroyuki Okazaki 32 50.9621
30 Michael Cameron 1 50.9234
31 Alen Kecic 14 50.9065
32 Thomas Ritschel 88 50.8707
33 Konstantin Agafonov 1 50.8197
34 Peter Benson 110 50.7155
35 Erik Veit 35 50.6305
36 Michael Schulz 1 50.5434
37 Karsten Klopffleisch 1 50.5009
38 Roman Vogt 3 50.4948
39 Ed Goforth 9 50.4785
40 Barry Schnur 4 50.4538

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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)).

Printed from the PrimePages <> © Chris Caldwell.