# What is the smallest prime?

• Published in 2012
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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.

### BibTeX entry

@article{Whatisthesmallestprime,
title = {What is the smallest prime?},
author = {Chris K. Caldwell and Yeng Xiong},
url = {http://arxiv.org/abs/1209.2007v2 http://arxiv.org/pdf/1209.2007v2},
urldate = {2016-07-05},
year = 2012,
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.},
comment = {},
archivePrefix = {arXiv},
eprint = {1209.2007},
primaryClass = {math.HO},
collections = {Easily explained,History,Notation and conventions,Integerology}
}