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What is the Smallest Prime?
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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.

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(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.

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