Computational Experiments in Number Theory

תקציר מקורי באנגליתarXiv:2504.19451v4 Announce Type: replace-cross Abstract: 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 ac