<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this article we introduce Proth numbers and prove two theorems on such numbers being prime [3]. We also give revised versions of Pocklington’s theorem and of the Legendre symbol. Finally, we prove Pepin’s theorem and that the fifth Fermat number is not prime.</p></abstract>

In this article we introduce Proth numbers and prove two theorems on such numbers being prime [3]. We also give revised versions of Pocklington’s theorem and of the Legendre symbol. Finally, we prove Pepin’s theorem and that the fifth Fermat number is not prime.

Proth Numbers

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

{"article-title":"Proth Numbers"}

In this article we introduce Proth numbers and prove two theorems on such numbers being prime [3]. We also give revised versions of Pocklington’s theorem and...

Proth Numbers

Published Online: Jun 30, 2014

Page range: 111 - 118

Received: Jun 09, 2014

DOI: https://doi.org/10.2478/forma-2014-0013

Keywords
prime numbers, Pocklington’s theorem, Proth’s theorem, Pepin’s theorem

© 2014 Christoph Schwarzweller

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

Proth Numbers

Published Online: Jun 30, 2014

Page range: 111 - 118

Received: Jun 09, 2014

DOI: https://doi.org/10.2478/forma-2014-0013

Keywordsprime numbers, Pocklington’s theorem, Proth’s theorem, Pepin’s theorem

© 2014 Christoph Schwarzweller

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

Keywords
prime numbers, Pocklington’s theorem, Proth’s theorem, Pepin’s theorem