# Number Theory

## 1405 Submissions

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

### Simplification of the Sieve of Eratosthenes

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

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

### Two Conjectures Involving the Sum of a Prime and a Factorial Number

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

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

### A Theorem for Knuth-Arrows

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

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

### A Conjecture on the Pairs of Primes p, q, Where Q is Equal to the Sum of P and a Primorial Number

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

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

### A Conjecture on Primes Involving the Pairs of Sexy Primes

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

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

### Ten Prime-Generating Quadratic Polynomials

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

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

### Seventeen Generic Formulas that May Generate Prime-Producing Quadratic Polynomials

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

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

### The Ultimate Proof to the Infinity of Twin Prime Numbers

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

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

### The Number System And Mathematics

Authors: Bertrand Wong
Comments: 2 Pages.

This article raises some important points about our number system and mathematics.
Category: Number Theory

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

### An Observation About the Digital Root of the Twin Primes, Few Conjectures and an Open Problem on Primes

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

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

### The Solution to the Beal's Conjecture

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

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

### Arithmetic Progression of More Squares

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

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

### The Pell Prime Conjectures

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

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

### On a Simpler, Much More General and Truly Marvellous Proof of Fermat's Last Theorem (II)

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

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

### Goldbach Conjecture Resolution

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

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

### Prime Numbers Finding Algorithm and Approval of the Conjecture of Twin Prim

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

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

### Are there Simple Proofs of Fermat's Last Theorem?

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