[6] **viXra:1206.0089 [pdf]**
*replaced on 2012-07-28 22:24:39*

**Authors:** Bertrand Wong

**Comments:** 9 Pages. Typographical correction has been carried out.

The author had published a paper on the solutions for the twin primes conjecture in an international mathematics journal in 2003. This paper, which consists of 2 parts that are each self-contained, presents some approaches to the twin primes problem.

**Category:** Number Theory

[5] **viXra:1206.0088 [pdf]**
*replaced on 2013-10-14 15:40:42*

**Authors:** Bertrand Wong

**Comments:** 16 Pages.

The author had published a paper on the solutions for the twin primes conjecture in an international mathematics journal in 2003. This paper, which consists of 5 parts that are each self-contained, presents strong arguments which support the validity of the twin primes conjecture.

**Category:** Number Theory

[4] **viXra:1206.0075 [pdf]**
*replaced on 2013-03-27 04:16:46*

**Authors:** Korn Rakpradit

**Comments:** 76 Pages.

Bernhard Riemann has written down a very mysterious work “Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse” since 1859. This paper of Riemann tried to show some functional equations related to prime numbers without proof. Let us investigate those functional equations together about how and where they came from. And at the same time let us find out whether or not the Riemann Zeta Function ζ(s)=2^s (π)^(s-1)sin(π s/2 )Г(1-s)ζ(1-s) really has zeroes at negative even integers (-2, -4 , -6 …), which are called the trivial zeroes, and the nontrivial zeroes of Riemann Zeta Function which are in the critical strip (0<ℜ(s)<1) lie on the critical line (ℜ(s) = 1/2) (or the nontrivial zeroes of Riemann Zeta Function are complex numbers of the form (1/2+∝i)).Step by step, you will not believe your eyes to see that Riemann has made such unbelievable mistakes in his work. Finally, you can easily find out that there are no trivial and nontrivial zeroes of Riemann zeta function at all.

**Category:** Number Theory

[3] **viXra:1206.0051 [pdf]**
*submitted on 2012-06-14 03:15:35*

**Authors:** Chun-Xuan Jiang

**Comments:** 6 Pages.

Jiang is a Chinese mathematician proponent of fringe scientific theories who works mostly in fierld of number theory.He disproved the Riemann hypothesis(1998),proved Fermat last theorem(1991) before Andrew Wiles(1994),proved the twin prime conjecture and Goldbach conjecture(1996),and proved alost all prime problems in prime distribution using Jiang function.China does not need epoch-making achievement . n the Great all of the peo[le in March 5,2002 He zuoxiu academician at the nine session of the five CPPCC meeting:Jiang study is pseudoscience

**Category:** Number Theory

[2] **viXra:1206.0025 [pdf]**
*submitted on 2012-06-07 03:50:33*

**Authors:** Vladimir Godovalov

**Comments:** 109 Pages. Russian version

Nature does not create anything extra. Mathematics as a part of Nature obeys the same law. If figurate numbers exist in nature, it means there is reason for their existence. In fact they represent a key to many solutions and serve as a foundation in Powers Fields Theory.
The theory opens a new chapter in mathematics, which studies interaction of monomials n^m in homogenous areas called the powers fields. More precisely, these areas consist of consecutive and interconnected values organized in rows by their common attribute – the exponent m itself. The theory is based on Monomial Decomposition Theorem which firstly leads to structural organization of said areas, secondly, settles the powers field’s basic equations and finally allows the areas elements be expressed as figurative and factorial polynomials. Because of that the nature of equation a^x+b^y=c^z becomes a not complicated subject to systematic analysis enabling the theory to reveal in detail its matter.
Technically the analysis falls in two ways. It begins with analysis of the powers field’s properties, the first of which actually states the Fermat’s conjecture. Being in fact not an independent problem by itself, Fermat’s conjecture is a technique applied in studying of the powers fields. Other powers field’s property, currently unknown to modern mathematics, is based on the genus-structural properties of figurative polynomials and therefore carries the same name. And finally, performing the most extensive study, the Beal’s conjecture ends analysis by searching solutions to the equations as well as determines among them cases with common prime factor.
In addition to studying the powers fields as a main objective, the theory introduces several innovative methods along with new functions and definitions. Also, the paper includes Composite Numbers Theorem, the proven results of which are well known in modern mathematics formulas of factoring sum/difference of n-powers.
The theory not only does discover many links within modern mathematics, it also raises a set of new questions in more specific areas of the theory and one of them for example is Phantom problem. The emergence of Powers Fields Theory not only fills a gap in Number Theory, but also sheds light on many related issues.

**Category:** Number Theory

[1] **viXra:1206.0016 [pdf]**
*replaced on 2012-06-07 15:21:04*

**Authors:** Hassan Mohammed Eweidah

**Comments:** 13 Pages.

A new theory in the field of number theory. For hundreds of years mathematicians could not reach a general formula for the prime numbers. But Now my discovery gives 4 general formulas produce all odd numbers except multiples of 3 and the prime numbers and by developing it, it will produce one formula gives all odd numbers except the prime numbers. Therefore this new theory would solve the problem of the difficulty in reaching the prime numbers.

**Category:** Number Theory