# Machine Learning of the Prime Distribution

arXiv: https://arxiv.org/abs/2403.12588 · HTML: https://mlsanity.com/paper/2403.12588/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 17 references that are in the map.
- First posted on arXiv 19 Mar 2024.

## Builds on (most cited first, 2 of 2)

- [Deep-Learning the Landscape](https://mlsanity.com/paper/1706.02714/) (2017)
- [Integer Factorisation, Fermat & Machine Learning on a Classical Computer](https://mlsanity.com/paper/2308.12290/) (2023)

## Built on by (most cited first, 1 of 1)

- [Testing Transformer Learnability on the Arithmetic Sequence of Rooted Trees](https://mlsanity.com/paper/2512.01870/) (2025)

## Abstract (arXiv)

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 ErdHos-Kac law would very unlikely be discovered by current machine learning techniques. Numerical experiments that we perform corroborate our theoretical findings.