[17] **viXra:1709.0428 [pdf]**
*submitted on 2017-09-28 17:54:57*

**Authors:** Peter Bissonnet

**Comments:** 13 Pages.

This paper again specifies the major points of the article “Do Prime Numbers
Obey a Three-Dimensional Double Helix?” [1] which was received on February
16, 2006 by Hadronic Journal. New information has been added and elucidated
upon, such as why the numbers 2 and 3 are not considered true prime
numbers, and why s in the following formulas for 6s − 1 and for 6s + 1 is really
a composite number equal to the sum of two other numbers, suggesting
that s is always to be considered as an integer. Other new information is added
as well, such as how an engineer in a matter of seconds decomposed a large
prime product into its constituent primes using basic software and won a
contract for his firm.

**Category:** Number Theory

[16] **viXra:1709.0417 [pdf]**
*submitted on 2017-09-28 08:14:22*

**Authors:** Ramón Ruiz

**Comments:** 26 Pages. This document is written in Spanish

Twin Primes Conjecture: “There are infinitely many primes p such that (p + 2) is also prime”.
In this document I have used the prime numbers theorem enunciated by Carl Friedrich Gauss and the prime numbers theorem in arithmetic progressions. These two theorems applied to a combination of two arithmetic progressions of module 30 that contain prime numbers, allows us to develop a nonprobability general formula to calculate, approximately, the number of prime pairs, p and (p + 2), that are lesser than a number x.
This research is based on a approach designed solely to demonstrate the Twin Prime Conjecture and the Binary Goldbach Conjecture.

**Category:** Number Theory

[15] **viXra:1709.0411 [pdf]**
*submitted on 2017-09-27 14:14:11*

**Authors:** John Smith

**Comments:** 7 Pages.

Abstract In 1963, a game show called Lets Make A Deal began in the United States. On the show, the host - Monty Hall - would present contestants with the choice of 3 doors, behind only 1 of which was a car. A contestant would pick a door such as No. 1, and Monty, who knew what was behind the doors, would open another door, say No. 2, revealing a goat. Monty would then ask the contestant if they wanted to change their selection to door No. 3. It is widely accepted that the contestant should change doors on the basis that the chances of the car being behind door 3 are 2/3, whereas the chances of the car being behind door 1 are only 1/3. But by appeal to congruities that exist between this seemingly innocuous and simple problem and variety of deeper and less tractable problems, the Monty Hall Problem is revealed as the tip of a great intellectual iceberg.

**Category:** Number Theory

[14] **viXra:1709.0410 [pdf]**
*submitted on 2017-09-27 14:15:31*

**Authors:** John Smith

**Comments:** 2 Pages.

In 1986 AndrewWiles published a ground-breaking proof of Fermat's Last Theorem. But in spite of the rarity and the significance of the achievement, the underlying reasoning is so convoluted that it would be be extremely difficult -if not impossible- for any but a tiny minority of specialists to understand it. Most must simply take the word of Wiles and his fellow experts that Fermat's Last Theorem has been proved. But the conjecture itself -that no 3 positive integers can satisfy the equation x^n + y^n = z^n for any positive-integer value of n greater than 2- is so simple that a school child could understand it, and Fermat himself claimed that he possessed a proof, one that -if it existed- must have been expressed in the language of 17th century mathematics, and the language of 21st century high school mathematics. Ye there can be no such proof: this note outlines a complimentary but alternative argument to that employed by Wiles that shows why no 17th century proof of the theorem is possible.

**Category:** Number Theory

[13] **viXra:1709.0408 [pdf]**
*submitted on 2017-09-27 19:45:24*

**Authors:** Johnny E Magee

**Comments:** 18 Pages.

Focusing on the properties and constraints of the decompositions of Fermat’s equation and its elements --and employing only basic arithmetic
and algebraic techniques that would have been known to Fermat-- we identify certain specific requirements necessary for c, of (an + bn) = cn,
to be an integer, and establish that these requirements can only be met at n = 2.
AMS Subject Classification (2010): Primary, 11D41
Key words and phrases: Fermat’s Last Theorem, Fermat’s Equation, Binomial Theorem

**Category:** Number Theory

[12] **viXra:1709.0375 [pdf]**
*submitted on 2017-09-24 18:23:32*

**Authors:** Matanari Shimoinuda

**Comments:** 28 Pages.

This article is the summary of the spectral interpretation of critical zeroes of an L-function by Alain Connes. I try to examine the subject from the view of the representation theory and add some comments.

**Category:** Number Theory

[11] **viXra:1709.0312 [pdf]**
*replaced on 2017-12-07 21:18:35*

**Authors:** Ihsan Raja Muda Nasution

**Comments:** 2 Pages.

In this paper, we find the axiomatic pattern of prime numbers.

**Category:** Number Theory

[10] **viXra:1709.0295 [pdf]**
*submitted on 2017-09-20 06:46:03*

**Authors:** Faisal Amin Yassein Abdelmohssin

**Comments:** 4 Pages.

Fermat’s zero theorem is stated as follows: It is impossible to separate a square of a difference of two natural numbers into two squares of differences, or a cube power of a difference into two cube powers of differences, or a fourth power of a difference into two fourth powers, or in general, any power higher than the first, into two like powers of differences.

**Category:** Number Theory

[9] **viXra:1709.0288 [pdf]**
*submitted on 2017-09-19 04:55:48*

**Authors:** Ranganath G. Kulkarni

**Comments:** 2 Pages.

A quadratic equation for prime numbers is assumed to be true that satisfy the following four rules. Some prime numbers violate these rules. Whereas some non prime numbers satisfy the four rules. They are not prime, therefore to make them violate the fourth rule we need to study how to choose the value of m and n so as make the quadratic equation as the primes generating formula.

**Category:** Number Theory

[8] **viXra:1709.0258 [pdf]**
*submitted on 2017-09-17 13:33:28*

**Authors:** Victor Sorokine

**Comments:** 2 Pages.

The essence of the contradiction. The hypothetical Fermat's equality is contradictory between
the second digits of the factors of the number А.

**Category:** Number Theory

[7] **viXra:1709.0257 [pdf]**
*submitted on 2017-09-17 13:35:16*

**Authors:** Victor Sorokine

**Comments:** 2 Pages. French version

The essence of the contradiction. The hypothetical Fermat's equality is contradictory between
the second digits of the factors of the number А.

L'égalité de Fermat est contradictoire entre les deuxièmes chiffres des facteurs du nombre A.

**Category:** Number Theory

[6] **viXra:1709.0256 [pdf]**
*submitted on 2017-09-17 13:36:32*

**Authors:** Victor Sorokine

**Comments:** 2 Pages. Russian version

The essence of the contradiction. The hypothetical Fermat's equality is contradictory between
the second digits of the factors of the number А.

Суть противоречия. Равенство Ферма противоречиво по вторым цифрам сомножителей числа А.

**Category:** Number Theory

[5] **viXra:1709.0227 [pdf]**
*submitted on 2017-09-15 05:23:56*

**Authors:** José Francisco García Juliá

**Comments:** 2 Pages.

It is obtained a minor theorem related with the Fermat conjecture.

**Category:** Number Theory

[4] **viXra:1709.0128 [pdf]**
*submitted on 2017-09-11 05:10:30*

**Authors:** Faisal Amin Yassein Abdelmohssin

**Comments:** 3 Pages.

Relationships among natural numbers constituting a Pythagorean triple (PT) and between these natural numbers constituting the Pythagorean triples (PTs) and Prime Numbers (PNs) have been found. These relationships are formulated as theorems; first theorem is that the natural numbers constituting a Pythagorean triple (PT) satisfy a certain equation related to sum of their differences; second theorem is that differences of sum of the natural numbers constituting a Pythagorean triple (PT) are prime numbers.

**Category:** Number Theory

[3] **viXra:1709.0092 [pdf]**
*submitted on 2017-09-08 12:19:26*

**Authors:** Edgar Valdebenito

**Comments:** 4 Pages.

This note presents some formulas for pi.

**Category:** Number Theory

[2] **viXra:1709.0013 [pdf]**
*submitted on 2017-09-02 03:44:43*

**Authors:** Zhang Tianshu

**Comments:** 25 Pages.

Let us regard positive integers which have a common prime factor as a kind, then the positive half line of the number axis consists of infinite many recurring line segments which have same permutations of c kinds of integers’ points, where c≥1. In this article we shall prove Grimm’s conjecture by the method which changes stepwise symbols of each kind of composite numbers’ points at the original number axis, so as to form consecutive composite numbers’ points inside the limited field of proven Legendre- Zhang conjecture as the true.

**Category:** Number Theory

[1] **viXra:1709.0003 [pdf]**
*submitted on 2017-09-01 07:17:32*

**Authors:** T.Nakashima

**Comments:** 1 Page.

In this paper, we prove Conway's problem.

**Category:** Number Theory