What is the smallest prime?

TL;DR

This paper surveys the historical evolution of the concept of the first prime number, focusing on how definitions of primality have changed over time and their implications.

Contribution

It provides a comprehensive historical analysis of the changing definitions of the first prime, highlighting key mathematicians and reasons for these shifts.

Findings

Historical definitions varied, with some including one as prime.

The first prime was often considered to be two or three in different eras.

Modern consensus is that two is the first prime number.

Abstract

What is the first prime? It seems that the number two should be the obvious answer, and today it is, but it was not always so. There were times when and mathematicians for whom the numbers one and three were acceptable answers. To find the first prime, we must also know what the first positive integer is. Surprisingly, with the definitions used at various times throughout history, one was often not the first positive integer (some started with two, and a few with three). In this article, we survey the history of the primality of one, from the ancient Greeks to modern times. We will discuss some of the reasons definitions changed, and provide several examples. We will also discuss the last significant mathematicians to list the number one as prime.