[17] **viXra:1405.0348 [pdf]**
*submitted on 2014-05-28 14:44:28*

**Authors:** Raffaele Cogoni

**Comments:** 4 Pages. The Sieve of Eratosthenes a simplified method to find the prime numbers, useful for middle school students and supperiori

Abstract
It is a procedure to find the prime numbers, in practice it is a simplification
the sieve of Eratosthenes

**Category:** Number Theory

[16] **viXra:1405.0336 [pdf]**
*submitted on 2014-05-28 05:50:51*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I state two conjectures about the sum of a prime and a factorial.

**Category:** Number Theory

[15] **viXra:1405.0284 [pdf]**
*submitted on 2014-05-21 20:06:40*

**Authors:** Sbiis Saibian

**Comments:** 32 Pages.

In 1976 Donald Knuth introduced the world to his so called "Up-arrow notation" for very large positive integers. In this paper I prove a simple theorem which allows one to easily compare expressions involving Up-arrows.

**Category:** Number Theory

[14] **viXra:1405.0278 [pdf]**
*submitted on 2014-05-20 16:14:43*

**Authors:** Marius Coman

**Comments:** 3 Pages.

In a previous paper I stated a conjecture on primes involving the pairs of sexy primes, which are the two primes that differ from each other by six. In this paper I extend that conjecture on the pairs of primes [p, q], where q is of the form p + p(n)#, where p(n)# is a primorial number, which means the product of first n primes.

**Category:** Number Theory

[13] **viXra:1405.0243 [pdf]**
*submitted on 2014-05-15 02:15:31*

**Authors:** Marius Coman

**Comments:** 1 Page.

This paper states a conjecture on primes involving two types of pairs of primes: the pairs of sexy primes, which are the two primes that differ from each other by six and the pairs of primes of the form [p, q], where q = p + 6*r, where r is positive integer.

**Category:** Number Theory

[12] **viXra:1405.0239 [pdf]**
*submitted on 2014-05-14 08:30:17*

**Authors:** Marius Coman

**Comments:** 8 Pages.

In two of my previous papers I treated quadratic polynomials which have the property to produce many primes in a row: in one of them I listed forty-two such polynomials which generate more than twenty-three primes in a row and in another one I listed few generic formulas which may conduct to find such prime-producing quadratic polynomials. In this paper I will present ten such polynomials which I discovered and posted in OEIS, each accompanied by its first fifty terms and some comments about it.

**Category:** Number Theory

[11] **viXra:1405.0238 [pdf]**
*submitted on 2014-05-14 04:02:08*

**Authors:** Marius Coman

**Comments:** 6 Pages.

In one of my previous papers I listed forty-two quadratic polynomials which generate more than twenty-three primes in a row, from which ten were already known from the articles available on Internet and thirty-two were discovered by me. In this paper I list few generic formulas which may conduct to find such prime-producing quadratic polynomials.

**Category:** Number Theory

[10] **viXra:1405.0221 [pdf]**
*submitted on 2014-05-12 20:02:57*

**Authors:** Marouane Rhafli

**Comments:** 5 Pages. A complementary file to my pdf on http://vixra.org/pdf/1405.0011v1.pdf

In this paper I’ll give another proof to the infinity of twin primes , I’ll prove that Lim Inf (Pn+1 – Pn ) =2

**Category:** Number Theory

[9] **viXra:1405.0204 [pdf]**
*submitted on 2014-05-10 00:44:08*

**Authors:** Bertrand Wong

**Comments:** 2 Pages.

This article raises some important points about our number system and mathematics.

**Category:** Number Theory

[8] **viXra:1405.0200 [pdf]**
*submitted on 2014-05-09 07:11:53*

**Authors:** Marius Coman

**Comments:** 2 Pages.

Few interesting properties which distinquish twin primes from the general set of primes there are already known. I wrote myself an article regarding an interesting property of a set of (pairs of) twin primes based on the sum of the digits of the lesser (implicitly greater) prime from a pair of twin primes. This paper notes a property regarding twin primes based on their digital root.

**Category:** Number Theory

[7] **viXra:1405.0195 [pdf]**
*submitted on 2014-05-07 18:20:48*

**Authors:** Marouane Rhafli

**Comments:** 8 Pages.

This study presents an approval to the Beal’s conjecture, we’ll show that this conjecture is true and give a formula that give the common prime factor, some testing examples will be exposed and the theorem is given at the end.

**Category:** Number Theory

[6] **viXra:1405.0026 [pdf]**
*submitted on 2014-05-05 12:32:49*

**Authors:** Muneer Jebreel Karama

**Comments:** 5 Pages.

The aim of this paper is presenting new arithmetic progressions among squares i.e. more than three squares, moreover to introduce arithmetic progression of higher power.

**Category:** Number Theory

[5] **viXra:1405.0025 [pdf]**
*submitted on 2014-05-05 13:12:33*

**Authors:** Al Kelley

**Comments:** 7 Pages.

Using the x increasing algorithm to select solutions d of the Pell equation, we generate an infinite sequence of integers that are conjectured to be primes. The sequence A033316 at oeis.org is closely related but not the same. Here is how our sequence of conjectured primes starts: 53, 61, 109, 181, 277, 397, 409, 421, ...

**Category:** Number Theory

[4] **viXra:1405.0023 [pdf]**
*replaced on 2015-07-08 04:57:05*

**Authors:** Golden Gadzirayi Nyambuya

**Comments:** 8 Pages. Proof must now be complete. Comments Welcome

English mathematics Professor, Sir Andrew John Wiles of the University of Cambridge finally and conclusively proved in 1995 Fermat's Last Theorem} which had for 358 years notoriously resisted all efforts to prove it. Sir Professor Andrew Wiles's proof employs very advanced mathematical tools and methods that were not at all available in the known World during Fermat's days. Given that Fermat claimed to have had the `truly marvellous' proof, this fact that the proof only came after 358 years of repeated failures by many notable mathematicians and that the proof came from mathematical tools and methods which are far ahead of Fermat's time, this has led many to doubt that Fermat actually did possess the `truly marvellous' proof which he claimed to have had. In this short reading, via elementary arithmetic methods which make use of Pythagoras theorem, we demonstrate conclusively that Fermat's Last Theorem actually yields to our efforts to prove it.

**Category:** Number Theory

[3] **viXra:1405.0014 [pdf]**
*submitted on 2014-05-02 16:30:38*

**Authors:** Marouane Rhafli

**Comments:** 6 Pages.

Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and in all
of mathematics.It states:Every even integer greater than 2 can be expressed as the sum of two primes.In this
study I’ll prove that this conjecture is true.

**Category:** Number Theory

[2] **viXra:1405.0011 [pdf]**
*submitted on 2014-05-01 17:50:51*

**Authors:** Marouane Rhafli

**Comments:** 14 Pages.

This study presents a new prime number finding algorithm,in this study we will build an algorithm that can find all the consecutive prime numbers in a given interval,we will see testing examples,in the second part of this study we will prove the twin prime numbers conjecture to be true and give an equation that can give percentage of primes in givdn interval

**Category:** Number Theory

[1] **viXra:1405.0008 [pdf]**
*submitted on 2014-05-01 19:40:49*

**Authors:** Victor Christianto

**Comments:** 2 Pages. This article has not been submitted yet to any journal. Comments are welcome.

Beside rigorous proofs of Fermat's last theorem, there are relatively simple approaches to arrive at the same conclusion. One of the simple proofs is by Pogorsky, available at http://vixra.org/abs/1209.0099.

**Category:** Number Theory