is there any research into or applications of machine learning in number theory?

am also looking for (leading examples of) statistical/empirical analysis of number theory questions. also wondering if genetic algorithms in particular have ever been used in these areas.

  • Let's assume the distribution of the primes is totally random (with known average density). What you're asking would be for SVM's, logistic regressions, and multilayer NN's to predict, better than random, something that has no pattern. Right? – isomorphismes Jun 19 '15 at 14:51
  • We already know to exclude anything not ending in 1,3,7,9. And further results like in a number theory book say others not to check for primality. But what you're looking for is something like "Derive implications like this one?" Maybe it would have to learn on symbols? – isomorphismes Jun 19 '15 at 14:57
up vote 6 down vote accepted

Genetic algorithms were used to lower the prime gap to 4680 in the recent Zhang twin primes proof breakthrough and associated Polymath project. The bound has been lowered by other methods but it shows some potential for machine learning approaches in this or related areas. they can be used to devise/optimize effective "combs" or basically sieves for analyzing/screening smallest-possible prime gaps.

Together and Alone, Closing the Prime Gap (Erica Klarreich, Quanta magazine, 19 November 2013):

The team eventually came up with the Polymath project’s record-holder — a 632-tooth comb whose width is 4,680 — using a genetic algorithm that “mates” admissible combs with each other to produce new, potentially better combs.

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