Machine Learning of the Prime Distribution

• URL: http://arxiv.org/abs/2403.12588v2
• Date: Sun, 2 Jun 2024 17:18:40 GMT
• Title: Machine Learning of the Prime Distribution
• Authors: Alexander Kolpakov, A. Alistair Rocke,
• Abstract summary: We provide a theoretical argument explaining the experimental observations of Yang-Hui He about the learnability of primes. We also posit that the ErdHos-Kac law would very unlikely be discovered by current machine learning techniques.
• Score: 49.84018914962972
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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