[8] **viXra:1202.0086 [pdf]**
*replaced on 2012-03-03 23:45:52*

**Authors:** Song Wen Miao

**Comments:** 3 Pages. CHINESE

ALL EYES ARE ON FERMAT LAST THEOREM WHO PROVED FORST

**Category:** Number Theory

[7] **viXra:1202.0085 [pdf]**
*submitted on 2012-02-28 04:04:30*

**Authors:** Predrag Terzich

**Comments:** 4 Pages.

We explore some properties of generalized Fermat primes of the form : F_n(2q)=(2q)^(2^n)+1 , where n > 1 and q is an odd prime number .

**Category:** Number Theory

[6] **viXra:1202.0067 [pdf]**
*submitted on 2012-02-19 15:28:34*

**Authors:** Carlos Giraldo Ospina

**Comments:** 2 Pages.

In this paper Legendre’s Conjecture and Brocard’s Conjecture are proved by determining the amount of prime numbers that are located between N^2 and (N+1)^2.

**Category:** Number Theory

[5] **viXra:1202.0063 [pdf]**
*submitted on 2012-02-18 19:13:46*

**Authors:** Germán Paz

**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.

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.

**Category:** Number Theory

[4] **viXra:1202.0061 [pdf]**
*submitted on 2012-02-18 21:49:14*

**Authors:** Germán Paz

**Comments:** 19 Pages. This paper was submitted to the Journal of Number Theory.

In this paper it is proved that for every positive integer 'k' there are infinitely many prime numbers of the form n^2+k. As a result, it is proved that there are infinitely many prime numbers of the form n^2+1. This document also proposes a new and important conjecture about prime numbers called 'Conjecture C'. If this conjecture is true, then Legendre’s Conjecture, Brocard’s Conjecture and Andrica’s Conjecture are all true, and also some other important results will be true. Previous papers (written in Spanish language) were reviewed and approved by Carlos Giraldo Ospina (Lic. Matemáticas, USC, Cali, Colombia). This person posted versions of these papers at his own personal website and at ABCdatos. You may search for those papers on the internet. You may also visit the websites that are mentioned in this paper.

**Category:** Number Theory

[3] **viXra:1202.0056 [pdf]**
*submitted on 2012-02-17 10:43:30*

**Authors:** Chun-Xuan Jiang

**Comments:** 6 Pages.

Using cmplex hyperbolic functions and complex trionometric functions ,we reapear the Fermat marvelus proofs for Fermat last theorem

**Category:** Number Theory

[2] **viXra:1202.0029 [pdf]**
*replaced on 2014-08-25 05:42:42*

**Authors:** Predrag Terzich

**Comments:** 5 Pages.

We present deterministic primality test for Fermat numbers . Essentially this test is similar to the Lucas-Lehmer primality test for Mersenne numbers

**Category:** Number Theory

[1] **viXra:1202.0024 [pdf]**
*submitted on 2012-02-10 06:54:39*

**Authors:** Predrag Terzich

**Comments:** 4 Pages.

We present a theorem concerning the form of Mersenne
numbers . We also discuss a closed form expression which links prime numbers and natural logarithms .

**Category:** Number Theory