Number Theory


Infinitely Many Prime Numbers of the Form Ap±b

Authors: Germán Paz

In this paper it is proved that if 'a' and 'b' are two positive integers which are coprime and also have different parity, then there are infinitely many prime numbers of the form ap + b (where 'p' is a prime number) and infinitely many prime numbers of the form ap - b. In particular, all this proves that there are infinitely many prime numbers of the form 2p + 1, which proves there are infinitely many Sophie Germain Prime Numbers. This document also contains Lic. Carlos Giraldo Ospina's solution to the Polignac's Conjecture and to the Twin Prime Conjecture, which is one of Landau's Problems. Previous papers (written in Spanish language) were reviewed and approved by Lic. C. G. Ospina and versions of those papers were posted by this person on his own website and on ABCdatos. You may search for the papers' titles on the internet. You may also visit the websites that are mentioned in this paper. This work was submitted to the Journal of Number Theory.

Comments: 32 Pages, 15 pages of tables. On the tables that appear from pages 8 to 22, the numbers that are located on the third column and have commas should rather have dots, since this work is written in English. This detail does not change results at all.

Download: PDF

Submission history

[v1] 2012-02-18 19:13:46

Unique-IP document downloads: 193 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus