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.

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Submission history

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

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