An information-theoretic proof of the Erd\H{o}s-Kac theorem
Information Theory
2025-05-13 v3 math.IT
Abstract
In this article we show that the Erd\H{o}s-Kac theorem, which informally states that the number of prime divisors of very large integers converges to a normal distribution, has an elegant proof via Algorithmic Information Theory.
Cite
@article{arxiv.2202.11694,
title = {An information-theoretic proof of the Erd\H{o}s-Kac theorem},
author = {Aidan Rocke},
journal= {arXiv preprint arXiv:2202.11694},
year = {2025}
}
Comments
There is an error in this paper that is addressed in arXiv:2308.10817