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

I 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.

roughly related question on other site: Why can machine learning not recognize prime numbers?

an area in number theory that seems to have had some statistical analysis, the Collatz conjecture.

possibly somewhat related, automated theorem proving.

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#### Best Answer

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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