Proth Numbers

Christoph Schwarzweller

Formalized Mathematics (2014)

  • Volume: 22, Issue: 2, page 111-118
  • ISSN: 1426-2630

Abstract

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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.

How to cite

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Christoph Schwarzweller. "Proth Numbers." Formalized Mathematics 22.2 (2014): 111-118. <http://eudml.org/doc/268757>.

@article{ChristophSchwarzweller2014,
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.},
author = {Christoph Schwarzweller},
journal = {Formalized Mathematics},
keywords = {prime numbers; Pocklington’s theorem; Proth’s theorem; Pepin’s theorem},
language = {eng},
number = {2},
pages = {111-118},
title = {Proth Numbers},
url = {http://eudml.org/doc/268757},
volume = {22},
year = {2014},
}

TY - JOUR
AU - Christoph Schwarzweller
TI - Proth Numbers
JO - Formalized Mathematics
PY - 2014
VL - 22
IS - 2
SP - 111
EP - 118
AB - 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.
LA - eng
KW - prime numbers; Pocklington’s theorem; Proth’s theorem; Pepin’s theorem
UR - http://eudml.org/doc/268757
ER -

References

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  12. [12] Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445–449, 1990. 
  13. [13] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501–505, 1990. 
  14. [14] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821–827, 1990. 
  15. [15] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67–71, 1990. 
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