Machine Learning of the Prime Distribution
Information Theory
2025-05-13 v2 Artificial Intelligence
Machine Learning
math.IT
Number Theory
Abstract
In the present work we use maximum entropy methods to derive several theorems in probabilistic number theory, including a version of the Hardy-Ramanujan Theorem. We also provide a theoretical argument explaining the experimental observations of Yang-Hui He about the learnability of primes, and posit that the Erd\H{o}s-Kac law would very unlikely be discovered by current machine learning techniques. Numerical experiments that we perform corroborate our theoretical findings.
Keywords
Cite
@article{arxiv.2403.12588,
title = {Machine Learning of the Prime Distribution},
author = {Alexander Kolpakov and Aidan Rocke},
journal= {arXiv preprint arXiv:2403.12588},
year = {2025}
}
Comments
10 pages; parts of arXiv:2308.10817 reworked and amended; author's draft; accepted in PLOS ONE