[10] **viXra:1302.0170 [pdf]**
*submitted on 2013-02-28 08:55:04*

**Authors:** Marius Coman

**Comments:** 6 Pages. A list with 23 interesting properties that I found regarding the number 561, in relation with other Carmichael numbers, other Fermat pseudoprimes to base 2, with primes or other integers.

Though is the first Carmichael number, the number 561 doesn’t have the same fame as the third absolute Fermat pseudoprime, the Hardy-Ramanujan number, 1729. I try here to repair this injustice showing few special properties of the number 561.

**Category:** Number Theory

[9] **viXra:1302.0164 [pdf]**
*submitted on 2013-02-25 14:35:28*

**Authors:** Ibrahima Sambegou Diallo

**Comments:** 27 Pages. Here is the first part of this demonstration, which will soon be complemented. For mathematicians, the main challenge is to judge whether or not to use the Chebotarev theorem and asymptotic formulas for solving the Goldbach hypothesis. Happy reading!

The Goldbach conjecture is a matter of quantity of partitions of even numbers. This is
a consequence of combined four tools: the Chebotarev's density theorem, the Inclusion–
exclusion principle, the Prime number theorem and the Algorithms for evaluating π(x). By
applying these tools on a family of arithmetic sequences, we can establish the validity of this
conjecture.

**Category:** Number Theory

[8] **viXra:1302.0144 [pdf]**
*submitted on 2013-02-21 09:18:58*

**Authors:** Marius Coman

**Comments:** 5 Pages. An overview on the relation between emirps and concatenation, also with respect for the author's special numbers, Fermat pseudoprimes

Observations on generating primes or products of very few primes from reversible primes and Carmichael numbers using the method of concatenation.

**Category:** Number Theory

[7] **viXra:1302.0136 [pdf]**
*submitted on 2013-02-20 10:19:29*

**Authors:** Wes Hansen

**Comments:** 7 Pages.

Abstract. We define the set of positive even integers, the set of prime numbers, and the Cartesian product on the set of prime numbers. We then define a set composed of the sums of all ordered pairs in the Cartesian product on the set of primes. Finally, we demonstrate the existence of a bijection between this set of sums and the set of positive even integers and conclude by demonstrating the existence of an identity between the domain and codomain of this bijection, thus closing the binary Goldbach Conjecture.

**Category:** Number Theory

[6] **viXra:1302.0130 [pdf]**
*submitted on 2013-02-19 12:17:49*

**Authors:** M. MADANI Bouabdallah

**Comments:** 04 Pages. French language

We try to prove the Conjecture on Prime Numbers
(n² +1) by elementary geometry by using Pythagore,Fermat,Euler,Lagrange and Gauss theorems.

**Category:** Number Theory

[5] **viXra:1302.0106 [pdf]**
*replaced on 2013-04-06 09:54:57*

**Authors:** Liu Ran

**Comments:** 14 Pages.

Odd prime density regularity
Odd composite number density regularity
The limitation of odd number is composite number
Natural number is limited
Prime is limited

**Category:** Number Theory

[4] **viXra:1302.0102 [pdf]**
*submitted on 2013-02-16 01:42:53*

**Authors:** Jinhua Fei

**Comments:** 10 Pages.

This paper use Nevanlinna second fundamental theorem of the value distribution theory , give an corollary of Riemann hypothesis.

**Category:** Number Theory

[3] **viXra:1302.0093 [pdf]**
*submitted on 2013-02-14 12:46:52*

**Authors:** Marius Coman

**Comments:** 13 Pages. Definition and applications of ACPOW chains of primes.

An interesting type of recurrent sequences of primes which could eventually lead to longer chains of successive primes than known Cunningham chains or CPAP’s . Few conjectures including a stronger version of Legendre’s conjecture and one regarding the Fermat primes. A classification of the set of primes.

**Category:** Number Theory

[2] **viXra:1302.0056 [pdf]**
*submitted on 2013-02-09 16:17:07*

**Authors:** Sidharth Ghoshal

**Comments:** 11 Pages.

The goal of the following document is to demonstrate a proof of the Twin Prime Conjecture by determining bounds for the number of twin prime pairs between a number and its square and then proving that the lower bound is always greater than 1 for sufficiently large numbers.

**Category:** Number Theory

[1] **viXra:1302.0028 [pdf]**
*submitted on 2013-02-05 09:16:20*

**Authors:** Marius Coman

**Comments:** 3 Pages. A formula which might lead to a corespondence (maybe even a bijection) between the set of primes and a subset of Poulet numbers.

An amazingly easy to formulate but rich in consequences property of Fermat pseudoprimes to base 2 (Poulet numbers).

**Category:** Number Theory