Bertrand's postulate and the existence of finite fields

TL;DR

This paper explains how the proof of Bertrand's postulate can be adapted to demonstrate the existence of finite fields, providing an accessible exposition of this mathematical connection.

Contribution

It presents an adaptation of Erdős–Ramanujan's proof to establish the existence of finite fields, bridging prime number theory and finite field theory.

Findings

Erdős–Ramanujan proof can be adapted for finite fields

Existence of finite fields can be shown using prime distribution

Provides an accessible exposition connecting prime theorems and finite fields

Abstract

This is an expository note discussing how the Erdos--Ramanujan proof of Bertrand's postulate may be adapted to show the existence of finite fields.