[14] **viXra:1502.0200 [pdf]**
*submitted on 2015-02-22 12:36:35*

**Authors:** Edigles Guedes

**Comments:** 7 pages.

We prove some estimates for von Mangold function, second Chebyshev function and Riemann’s J function by elementary methods.

**Category:** Number Theory

[13] **viXra:1502.0198 [pdf]**
*submitted on 2015-02-22 14:58:04*

**Authors:** Waldemar Puszkarz

**Comments:** 2 Pages.

We propose a new mathematical constant related to the gaps between consecutive primes obtained by concatenating the digits in the prime gap numbers.

**Category:** Number Theory

[12] **viXra:1502.0197 [pdf]**
*submitted on 2015-02-22 07:53:46*

**Authors:** Rodolfo A. Nieves Rivas

**Comments:** 7 Pages.

In this brief paper we present the necessary and sufficient conditions within the solution of the Erdos-Straus conjecture when (n) takes the values of any twin prime. Then we conclude with a table for its visualization and analysis proving by the Bayes' theorem that the twin primes are infinite.

**Category:** Number Theory

[11] **viXra:1502.0195 [pdf]**
*submitted on 2015-02-22 06:05:29*

**Authors:** Alexander Fedorov

**Comments:** 37 Pages.

\
heIn this paper is offered and theoretically is based the algorithm
permissive with the lp of small number of arithmetic operations
with arbitrary positive integer(N) to answer a question : is N
composite or prime? The algorithm has a high operational speed
which depends a little on value N ,and is based on The method of
structurization of a set of positive integers (Np)
developed by the author. In limits of a framework of this method
is defined a special set of the structured integers (Ns) in which
it becomes possibility for testing of any structured integers (Sn)
on a membership of a set of composite structured integers (Nsc).
Between by Np and Ns is established one-to-one correspondence :
composite structured integers (Snc) are corresponded to composite
positive integers . Prime structured integers
are corresponded to prime positive integers
Thus for testing arbitrary (N) it is necessary to map it into .
Then we test obtained on a membership of
If Sn is a member of then the output follows
that tested N is also composite.If Sn is not a member of Nsc
then the output follows that tested $N$ is also prime , since if Sn
is not composite then it is prime ,tertiary is not given.

**Category:** Number Theory

[10] **viXra:1502.0140 [pdf]**
*submitted on 2015-02-16 16:09:21*

**Authors:** Edigles Guedes

**Comments:** 5 pages.

I proved two approximations for prime numbers using trigonometric sums.

**Category:** Number Theory

[9] **viXra:1502.0136 [pdf]**
*submitted on 2015-02-16 19:49:22*

**Authors:** Edigles Guedes

**Comments:** 3 pages.

I proved two lower bound for rst Chebyshev function and leave a conjecture on prime numbers.

**Category:** Number Theory

[8] **viXra:1502.0134 [pdf]**
*submitted on 2015-02-16 21:36:07*

**Authors:** Edigles Guedes

**Comments:** 3 pages.

We write a prove for Oppermann's conjecture using the Hardy-Wright's estimate for prime-counting function.

**Category:** Number Theory

[7] **viXra:1502.0131 [pdf]**
*submitted on 2015-02-16 13:02:14*

**Authors:** Edigles Guedes

**Comments:** 7 pages.

I proved some three approximations for prime numbers.

**Category:** Number Theory

[6] **viXra:1502.0078 [pdf]**
*replaced on 2015-02-17 05:25:35*

**Authors:** Zhenghai Song

**Comments:** 5 Pages.

Chunxuan Jiang is a tragic mathematician in the history of modern mathematics.In China Jiang work was completely repelled and been considered as pseudoscience.Jiang dedicates his work to alma mater (Beihang university) and China which rejected.

**Category:** Number Theory

[5] **viXra:1502.0039 [pdf]**
*submitted on 2015-02-04 23:56:09*

**Authors:** Posey Bonennnn, Posey Bonennn, Posey Bonenn, Posey Bonen

**Comments:** 1 Page.

ZFC IS WEEEEKK NEEDS MORE POWER> I CAN FIX THAT> I INTRODUCE A GENIUS AXIUM THAT SOLVES SEVERAL NOW TRIVIAL CONJECTURES THAT HAVE BEEN LONG STANDING. IT ALSO MAKES POSSIBLY IT TO PROOVE CONTINUOUM HYPOTHESIS AND THAT ZFC IS COMPLETE WITH MY NEW AXIUM>>>\\\\\\
THE AXEIUM IS THAT ZFC IS COMPLETE>

**Category:** Number Theory

[4] **viXra:1502.0038 [pdf]**
*submitted on 2015-02-04 23:57:46*

**Authors:** Posey Bonennn

**Comments:** 1 Page.

ZFC IS WEEEEKK NEEDS MORE POWER> I CAN FIX THAT> I INTRODUCE A GENIUS AXIUM THAT SOLVES SEVERAL NOW TRIVIAL CONJECTURES THAT HAVE BEEN LONG STANDING. IT ALSO MAKES POSSIBLY IT TO PROOVE CONTINUOUM HYPOTHESIS AND THAT ZFC IS COMPLETE WITH MY NEW AXIUM>>>\\\\\\
THE AXEIUM IS THAT ZFC IS COMPLETE>

**Category:** Number Theory

[3] **viXra:1502.0037 [pdf]**
*submitted on 2015-02-05 02:10:04*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In seven of my previous papers, I defined the MC function and I showed some of its possible applications. In this paper I present new interesting properties of other three Smarandache type sequences analyzed through the MC function.

**Category:** Number Theory

[2] **viXra:1502.0020 [pdf]**
*submitted on 2015-02-02 18:42:28*

**Authors:** Marius Coman

**Comments:** 1 Page.

In this paper I conjecture that for any pair of twin primes p and p + 2 there exist an odd positive integer n such that the value of Smarandache function for n is equal to p and the value of MC function for n is equal to p + 2.

**Category:** Number Theory

[1] **viXra:1502.0008 [pdf]**
*submitted on 2015-02-01 07:16:14*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In few of my previous papers I defined the MC function. In this paper I make a classification of primes in four classes using a formula involving this function, id est the formula p + MC(p + 2) – 5, where p is prime. The classification is strict, a prime can not belong simultaneously to two classes.

**Category:** Number Theory