English

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.

Keywords

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