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by tchitra
2963 days ago
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This seems extremely contrived and at best misleading, if it is meant to be more than an exercise to teach someone to code. If there were a function that could produce subsets of primes in a sequence via a C-infinity function (as you are doing via your trained neural net), then it is extremely, extremely unlikely that all of the known pseudo-randomness properties of prime numbers and their k-point functions are true. In some ways, this would be a sort of converse to the Green-Tao theorem --- one can 'easily' produce subsets of primes contained in arithmetic or geometric sequences. Can you provide a better justification for this project? I tend to find 'approximating primes via neural networks' as a silly combination of buzzwords that ignores all of the known facts about primes. At best, this project appears to perform a numerical experiment of the claim, "For all epsilon > 0, there exists an easy to compute C-infinity function (that can depend on epsilon) that can take an arithmetic/geometric/arithmetico-geometric sequence and produce, with high probability, a subset of primes of this sequence whose volume relative to all primes in this sequence is at least 1 - epsilon" Why should one believe that this is true? |
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If you do the minimal to avoid obvious non-primes, avoiding numbers divisible by 2 or 5, you can expect to find a N-digit prime checking about N random N-digit numbers (1), so finding a 4,000-digit one after experimenting for a while doesn’t indicate ability to find primes.
(1) the density of primes around 10ⁿ is about 1/ln(10ⁿ), so you expect to find a prime after ln(10ⁿ) random samples, and
Avoiding even numbers and multiples of five gives you back a factor of 2.5, more than offsetting that factor of ln(10)