Machine Learning of the Prime Distribution
<|reference_start|>Machine Learning of the Prime Distribution: 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.<|reference_end|>
@article{kolpakov2024machine,
    title={Machine Learning of the Prime Distribution},
    author={Alexander Kolpakov, A. Alistair Rocke},
    journal={arXiv preprint arXiv:2403.12588},
    year={2024},
    doi={10.1371/journal.pone.0301240},
    archivePrefix={arXiv},
    eprint={2403.12588},
    primaryClass={cs.IT cs.AI cs.LG math.IT math.NT}
}