<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

Publié en ligne: 30 juin 2014

Pages: 111 - 118

Reçu: 09 juin 2014

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

Mots clés
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

Publié en ligne: 30 juin 2014

Pages: 111 - 118

Reçu: 09 juin 2014

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

Mots clésprime 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)

Mots clés
prime numbers, Pocklington’s theorem, Proth’s theorem, Pepin’s theorem