[11] **viXra:1308.0122 [pdf]**
*replaced on 2013-08-28 08:48:38*

**Authors:** Yibing Qiu

**Comments:** 6 Pages.

Abstract
This article puts forward a new theorem concerns the distribution of prime numbers: Let
integer n≥4, there exist two distinct odd primes p and q such that n﹣p＝q﹣n. Proves the
theorem establish applied the Congruence theory and the Fermat's method of infinite
descent. With the application of the theorem, reaches several results.

**Category:** Number Theory

[10] **viXra:1308.0109 [pdf]**
*submitted on 2013-08-20 12:15:04*

**Authors:** Julien Laurendeau

**Comments:** 2 Pages. If you read this paper,pay a particularly strong attention on the end.

I will here state a conjecture of my own that will normally be so hard to prove as the Beal conjecture and Fermat’s last theorem.

**Category:** Number Theory

[9] **viXra:1308.0084 [pdf]**
*submitted on 2013-08-17 07:27:14*

**Authors:** Julien Laurendeau

**Comments:** 2 Pages.

I will here conjecture and prove using formulas.

**Category:** Number Theory

[8] **viXra:1308.0077 [pdf]**
*submitted on 2013-08-15 10:34:17*

**Authors:** Lenient T Tavengwa

**Comments:** 2 Pages.

The twin primes conjecture asserts that there are infinitely many primes p such that p + 2 is
also prime. The present paper proves that.

**Category:** Number Theory

[7] **viXra:1308.0074 [pdf]**
*submitted on 2013-08-14 13:04:58*

**Authors:** Th. Guyer

**Comments:** 1 Page.

Euklid's Theorem (of the infinite of the PrimeNumbers) is given; where p=prim and the TwinPrime(s) are called PrimeAngels.
So P(rime)=P(rime) / P(rime)=N(o)P(rime); P/=NP is no longer available and the problem was hard for more than 2000 years!

**Category:** Number Theory

[6] **viXra:1308.0071 [pdf]**
*submitted on 2013-08-14 00:20:19*

**Authors:** Kairbek Kazbekov

**Comments:** 27 Pages.

Horizontal and vertical distributions of complex zeros of the Riemann zeta-function in the
critical region are being found in general form in the paper on the basis of standard methods of
function theory of complex variable.

**Category:** Number Theory

[5] **viXra:1308.0055 [pdf]**
*replaced on 2013-09-06 02:23:31*

**Authors:** Zhen Liu

**Comments:** 12 Pages.

Using the method for equation reconstruction of prime sequence, this paper gives the proof that there are infinitely many primes of the form αβn+χ ,αnβ+χ and αβ1nmβ2+χ.

**Category:** Number Theory

[4] **viXra:1308.0045 [pdf]**
*submitted on 2013-08-08 21:01:21*

**Authors:** Edigles Guedes

**Comments:** 2 Pages.

We use the contradiction method for prove that the Catalan’s constant is irrational.

**Category:** Number Theory

[3] **viXra:1308.0032 [pdf]**
*submitted on 2013-08-05 18:39:33*

**Authors:** Dmitri Abramov

**Comments:** 5 Pages.

This article will define the range in which there is at least one pair of odd primes that when added produce specific even number. It will prove that every even number in that range can be written as a sum of at least one pair of odd primes. Additionally, this paper will prove trivial soft versions of Goldbach's conjecture that follow from the hard version.

**Category:** Number Theory

[2] **viXra:1308.0026 [pdf]**
*replaced on 2013-09-20 09:07:16*

**Authors:** Alexander Fedorov

**Comments:** 25 Pages.

One of causes why Twin Primes problem was
unsolved over a long period is that
pairs of Twin Primes (PTP) are considered separately
from other pairs of Twin Numbers (PTN).
By purpose of this work is research of connections
between different types of PTN. For realization of this
purpose by author was developed the "Arithmetic of
pairs of Twin Numbers" (APTN).
In APTN are defined three types PTN.
As shown in APTN all types PTN are connected with
each other by relations which represent distribution of
prime and composite positive integers less than n
between them.
On the basis of this relations (axioms APTN) are
deduced formulas for computation of the number of PTN
(NPTN) for each types.
In APTN also is defined and computed Average value
of the number of pairs are formed from odd prime
and composite positive integers $ < n $ . Separately
AVNPP for prime and AVNPC for composite positive integers.
We also deduced formulas for computation of deviation
NPTN from AVNPP and AVNPC.
It was shown that if $n$ go to infinity then NPTN go to AVNPC or AVNPP
respectively that permit to apply formulas for AVNPP and AVNPC
to computation of NPTN.
At the end is produced the proof of the Twin Primes
problem with help of APTN.
It is shown that if n go to infinity then NPTP go to infinity.

**Category:** Number Theory

[1] **viXra:1308.0007 [pdf]**
*submitted on 2013-08-01 17:50:20*

**Authors:** Marius Coman

**Comments:** 2 Pages.

Starting from the observation that the number 13^2 + 81*13 + 3*13*41 is a Poulet number (2821), and the number 41^2 + 81*41 + 3*13*41 is a Poulet number too (6601), and following my interest for the number 30, I found a formula that generates such pairs of Poulet numbers like (2821,6601).

**Category:** Number Theory