An information-theoretic proof of the Erd\H{o}s-Kac theorem

TL;DR

This paper presents an elegant proof of the Erdős-Kac theorem using Algorithmic Information Theory, linking number theory and information theory in a novel way.

Contribution

It introduces a new proof technique for the Erdős-Kac theorem based on Algorithmic Information Theory, offering deeper theoretical insights.

Findings

Erdős-Kac theorem proven via information-theoretic methods

Number of prime divisors converges to a normal distribution

New connections between number theory and information theory

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.