Top persons sorted by score (Another of the Prime Pages' resources)

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.

rank person primes score 142 Oscar Tutusaus Santandreu 9 46.2678 143 Rodger M. Ewing 4 46.2659 144 John Cosgrave 3 46.2586 145 Simeon I. B. Ayeni 4 46.2577 146 Tom Pepper 12 46.2543 147 Bartlett Henderson 12 46.2436 148 Robert Johnson 8 46.2209 149 John Jacobs 2 46.2019 150 Seiya Tsuji 1 46.1963 151 Ryan English 2 46.1926 152 Gerald C. Snyder 2 46.1836 153 Sascha Beat Dinkel 8 46.1769 154 Scott Yoshimura 1 46.1681 155 Steven Wong 6 46.1530 156 Jeff Anderson-Lee 7 46.1386 157 Alexander Gramolin 5 46.1080 158 Michael Angel 10 46.0906 159 Michael Reifschneider 9 46.0832 160 Peter Grobstich 6 46.0730 161 Ronny Willig 3 46.0552

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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)).