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arXiv:1209.2007math.HO

What is the smallest prime?

Chris K. Caldwell, Yeng Xiong

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.

arXiv comments
11 pages, 5 figures
Journal reference
J. Int. Seq., Vol. 15 (2012), Article 12.9.7
DOI
Subjects
math.HOHistory and Overview math.NTNumber Theory

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  1. Quadratic Reciprocity: The connection that changed number theory 1 comment

    • Some good answers and discussion at https://math.stackexchange.com/questions/120/why-is-1-not-a-... In particular, the papers "What is the smallest prime?" https://arxiv.org/abs/1209.2007 and "The History of the Primality of One: A Selection of Sources"…

      svatView on HNParent context

  2. Code Llama, a state-of-the-art large language model for coding 1 comment

    • Whether 1 should be a prime number or not wasn't clear-cut for centuries. Current consensus has settled on excluding 1 from the definition, but there are examples of publications well into the 20th century that still included 1 as prime. Fascinating read about the subject…

      RenaudView on HNParent context

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