# Computational Experiments in Number Theory

arXiv: https://arxiv.org/abs/2504.19451 · HTML: https://mlsanity.com/paper/2504.19451/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 20 references that are in the map.
- First posted on arXiv 28 Apr 2025.

## Builds on (most cited first, 10 of 10)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving](https://mlsanity.com/paper/2309.17452/) (2023)
- [Can LLMs Master Math? Investigating Large Language Models on Math Stack Exchange](https://mlsanity.com/paper/2404.00344/) (2024)
- [Machine-Learning the Sato--Tate Conjecture](https://mlsanity.com/paper/2010.01213/) (2020)
- [Hint-before-Solving Prompting: Guiding LLMs to Effectively Utilize Encoded Knowledge](https://mlsanity.com/paper/2402.14310/) (2024)
- [Give me a hint: Can LLMs take a hint to solve math problems?](https://mlsanity.com/paper/2410.05915/) (2024)

## Abstract (arXiv)

This paper presents two concrete applications of Artificial Intelligence to algorithmic and analytic number theory. Recent benchmarks of large language models have mainly focused on general mathematics problems and the currently infeasible objective of automated theorem proving. In the first part of this paper, we relax our ambition and focus on a more specialized domain: we evaluate the performance of the state-of-the-art open-source large language model Qwen2.5-Math-7B-Instruct on algorithmic and computational tasks in algorithmic number theory. On a benchmark of thirty algorithmic problems and thirty computational questions taken from classical number-theoretic textbooks and Math StackExchange, the model achieves at least 0.95 accuracy (relative to the true answer) on every problem or question when given an optimal non-spoiling hint. The second part of the paper empirically verifies a folklore conjecture in analytic number theory stating that the modulus (q) of a Dirichlet character (chi) is uniquely determined by the initial nontrivial zeros (ρ1,dots,ρk) (for some (k∈mathbbN)) of the corresponding Dirichlet (L)-function (L(s,chi)). We train a LightGBM multiclass classifier to predict the conductor (q) for 214 randomly chosen Dirichlet (L)-functions from a vector of statistical features of their initial zeros (moments, finite-difference statistics, FFT magnitudes, etc.). The model empirically verifies the conjecture for small (q), achieving at least 93.9% test accuracy when sufficient statistical properties of the zeros are incorporated. For the second part of the paper, code and dataset are available.