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 321 Frederik Schiøler 4 48.1595 322 Evelyn Chew 4 48.1508 323 Ben Meekins 2 48.1473 324 Scottie Mckinley 1 48.1415 325 Pietari Snow 5 48.1313 326 Joshua Brown 4 48.1281 327 Samuel VISCAPI 1 48.1273 328 Michele T. Mazzucato 4 48.1207 329 Eric Eskam 5 48.1206 330 Andreas Jourdan 4 48.0816 331 Vince Splain 5 48.0769 332 James Adrian 1 48.0751 333 Kenneth J. Brazier 3 48.0593 334 James Early 4 48.0507 335 James Boerner 3 48.0503 336 Vassili Koriabine 4 48.0497 337 Yegor Ryabchikov 1 48.0393 338 Kenneth Egtved Pedersen 4 48.0384 339 Szymon Banka 1.3333 48.0294 340 Reiner Elgetz 4 48.0222

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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)).