## 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

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