The distribution of primes and Euler characreristic

TL;DR

This paper explores the distribution of prime numbers through topology, introduces a conjecture equivalent to the Riemann Hypothesis, and aims to provide a new perspective on this longstanding problem.

Contribution

It proposes a topological conjecture that is shown to be equivalent to the Riemann Hypothesis, linking number theory and topology.

Findings

Conjecture equivalent to the Riemann Hypothesis

New topological perspective on prime distribution

Potential pathway to proving the Riemann Hypothesis

Abstract

We study the distribution of primes from a topological viewpoint. Certain conjecture is introduced, and we show that it is equivalent to the Riemann Hypothesis.