Title
A Prime Testing Algorithm from Leonhard Euler
Document Type
Article
Department or Administrative Unit
Mathematics
Publication Date
9-23-2021
Abstract
In 1749, Leonhard Euler solved a longstanding open problem in number theory, proving Fermat’s 1640 conjecture that any prime number of the form 4m + 1 can be written as the sum of two squares. This achievement overshadowed an equally impressive calculation that Euler devised at the same time, to test numbers for primality. In this article, we explore Euler’s primality test, demonstrating its computational parity with trial division, at least for a class of testable numbers. Additionally, we will see that primality testing was one of Euler’s lifelong interests, and was a topic he returned to time and again as an application of his number theory work.
Recommended Citation
Klyve, D., & Tou, E. R. (2021). A Prime Testing Algorithm from Leonhard Euler. The American Mathematical Monthly, 128(8), 687–700. https://doi.org/10.1080/00029890.2021.1943118
Journal
The American Mathematical Monthly
Copyright
© THE MATHEMATICAL ASSOCIATION OF AMERICA
Comments
This article was originally published in The American Mathematical Monthly. The full-text article from the publisher can be found here.
Due to copyright restrictions, this article is not available for free download from ScholarWorks @ CWU.