# Integer Factorisation, Fermat & Machine Learning on a Classical Computer

arXiv: https://arxiv.org/abs/2308.12290 · HTML: https://mlsanity.com/paper/2308.12290/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 26 references that are in the map.
- First posted on arXiv 16 Jul 2023.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)

## Built on by (most cited first, 2 of 2)

- [Machine Learning of the Prime Distribution](https://mlsanity.com/paper/2403.12588/) (2024)
- [Testing Transformer Learnability on the Arithmetic Sequence of Rooted Trees](https://mlsanity.com/paper/2512.01870/) (2025)

## Abstract (arXiv)

In this paper we describe a deep learning--based probabilistic algorithm for integer factorisation. We use Lawrence's extension of Fermat's factorisation algorithm to reduce the integer factorisation problem to a binary classification problem. To address the classification problem, based on the ease of generating large pseudo--random primes, a corpus of training data, as large as needed, is synthetically generated. We will introduce the algorithm, summarise some experiments, analyse where these experiments fall short, and finally put out a call to others to reproduce, verify and see if this approach can be improved to a point where it becomes a practical, scalable factorisation algorithm.