Journal of Integer Sequences, Vol. 15 (2012), Article 12.9.7

## What is the Smallest Prime?

### Chris K. Caldwell Department of Mathematics and Statistics University of Tennessee at Martin Martin, TN 38238 USA Yeng Xiong Department of Mathematics and Statistics University of Tennessee at Martin Martin, TN 38238 USA

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.

Full version:  pdf,    dvi,    ps,    latex

(Concerned with sequences A000027 A000040 A008578.)

Received September 27 2012; revised version received November 18 2012. Published in Journal of Integer Sequences, December 27 2012.