[15] **viXra:1311.0203 [pdf]**
*submitted on 2013-11-30 04:15:06*

**Authors:** Dmitri Abramov

**Comments:** 5 Pages.

This paper derives a function that estimates number of unique ways you can write z as z = p + q, where p and q are prime numbers, for every z E N that can be written in that form.

**Category:** Number Theory

[14] **viXra:1311.0179 [pdf]**
*submitted on 2013-11-27 04:20:58*

**Authors:** Marius Coman

**Comments:** 3 Pages.

In this paper I present a formula based on 2-Poulet numbers which seems to conduct always to a prime, a square of prime or a semiprime, a conjecture that this formula is generic for 2-Poulet numbers, and, in case that the conjecture doesn’t hold, I present another utility for this formula, namely to generate sequences of n-Poulet numbers.

**Category:** Number Theory

[13] **viXra:1311.0176 [pdf]**
*submitted on 2013-11-26 06:51:46*

**Authors:** Marius Coman

**Comments:** 2 Pages.

The lenght of the period of the rational number which is the sum, from n = 1 to n = ∞, of the numbers 1/(Cn – 1), where {C1, C2, ..., Cn} is the ordered set of Carmichael numbers, i.e. {561, 1105, 1729, 2465, ...}, seems to be always multiple of 66. This property doesn’t apply always when C1, C2, ..., Cn are not consecutive, so this pattern could be a way to determinate if between two known Carmichael numbers there exist other unknown Carmichael numbers.

**Category:** Number Theory

[12] **viXra:1311.0172 [pdf]**
*submitted on 2013-11-26 00:01:06*

**Authors:** Marius Coman

**Comments:** 3 Pages.

By playing with one of my favorite class of numbers, Poulet numbers, and one of my favorite operation, concatenation, I raised to myself few questions that seem interesting, worthy to share. I also conjectured that, reiterating a certain operation which will be defined, eventually for every Poulet number it will be find a corresponding prime. Then I extrapolated the conjecture for all composite positive integers.

**Category:** Number Theory

[11] **viXra:1311.0140 [pdf]**
*replaced on 2013-11-27 18:51:46*

**Authors:** Roberto Luis Recalde

**Comments:** 18 Pages. The third version of this work involves fixes made in the second one and a better explanation of the work itself, to a better understanding.

In this paper, we discover a new technique to build quadratic sequences wich converge to a number in the form K(2^(1/2)).

**Category:** Number Theory

[10] **viXra:1311.0137 [pdf]**
*submitted on 2013-11-19 10:58:04*

**Authors:** Marius Coman

**Comments:** 3 Pages.

I was following an interesting “track”, i.e. the pairs of primes [p,q] that apparently can form strictly Carmichael numbers of the form p*q*(n*(q – 1) + p), like for instance [23,67] and [41,241], when I observed that also all the Poulet numbers P which have the numbers p = 30*k + 23 and q = 90*k + 67 respectively p = 30*k + 11 and q = 180*k + 61 as prime factors can be written as P = p*q*(n*(q – 1) + p) and I made few conjectures.

**Category:** Number Theory

[9] **viXra:1311.0112 [pdf]**
*submitted on 2013-11-15 17:49:13*

**Authors:** Angel Garcés Doz

**Comments:** Pages.

This paper presents a possible elementary proof of the Riemann hypothesis. We say possible or potential, you have to be very cautious and skeptical of the potential of the evidence presented, is free of a crucial error that
invalidate the proof. After several months of extensive review, the author, having found no error we have decided to publish it in the hope that someone will find the error. However, it is considered that the method may be useful in some way. This potential proof uses
only the rudiments of analysis and arithmetic inequalities.
It includes a first part of the reason why we think that the Riemann hypothesis seems to be true.

**Category:** Number Theory

[8] **viXra:1311.0104 [pdf]**
*replaced on 2013-11-15 10:10:07*

**Authors:** Maik Becker-Sievert

**Comments:** 1 Page.

Proof Beal Concecture over circle radius 1

**Category:** Number Theory

[7] **viXra:1311.0097 [pdf]**
*replaced on 2013-11-16 03:39:24*

**Authors:** Marius Coman

**Comments:** 135 Pages. Published by Education Publishing, USA. Copyright 2013 by Marius Coman.

About the works of Florentin Smarandache have been written a lot of books (he himself wrote dozens of books and articles regarding math, physics, literature, philosophy). Being a globally recognized personality in both mathematics (there are countless functions and concepts that bear his name) and literature, it is natural that the volume of writings about his research is huge. What we try to do with this encyclopedia is to gather together as much as we can both from Smarandache’s mathematical work and the works of many mathematicians around the world inspired by the Smarandache notions. We structured this book using numbered Definitions, Theorems, Conjectures, Notes and Comments, in order to facilitate an easier reading but also to facilitate references to a specific paragraph. We divided the Bibliography in two parts, Writings by Florentin Smarandache (indexed by the name of books and articles) and Writings on Smarandache notions (indexed by the name of authors). We treated, in this book, about 130 Smarandache type sequences, about 50 Smarandache type functions and many solved or open problems of number theory. We also have, at the end of this book, a proposal for a new Smarandache type notion, id est the concept of “a set of Smarandache-Coman divisors of order k of a composite positive integer n with m prime factors”, notion that seems to have promising applications, at a first glance at least in the study of absolute and relative Fermat pseudoprimes, Carmichael numbers and Poulet numbers. This encyclopedia is both for researchers that will have on hand a tool that will help them “navigate” in the universe of Smarandache type notions and for young math enthusiasts: many of them will be attached by this wonderful branch of mathematics, number theory, reading the works of Florentin Smarandache.

**Category:** Number Theory

[6] **viXra:1311.0091 [pdf]**
*submitted on 2013-11-12 05:27:20*

**Authors:** Hashem Sazegar

**Comments:** 8 Pages.

In 1742, Goldbach claimed that each even number can be shown by two primes.
In 1937, Vinogradoff Russian Mathematician proved that each odd large
number can be shown by three primes. In 1930, Lev Schnirelmann proved that
each natural number can be shown by M-primes. In 1973, Chen Jingrun proved
that each odd number can be shown by one prime plus a number that has
maximum two primes. In this article, we state one proof for Goldbach's conjecture

**Category:** Number Theory

[5] **viXra:1311.0083 [pdf]**
*submitted on 2013-11-11 23:08:39*

**Authors:** Yibing Qiu

**Comments:** 1 Page.

Abstract：This article puts forward a proposition concerns twin primes.

**Category:** Number Theory

[4] **viXra:1311.0072 [pdf]**
*submitted on 2013-11-11 04:52:03*

**Authors:** Maik Becker-Sievert

**Comments:** 1 Page.

Sum and Difference of Square Numbers

**Category:** Number Theory

[3] **viXra:1311.0069 [pdf]**
*submitted on 2013-11-10 13:20:39*

**Authors:** Edigles Guedes

**Comments:** 9 Pages.

The main objective of this paper is to develop an infinite product formula for the ratio of consecutive prime numbers, using Jacobi elliptic functions.

**Category:** Number Theory

[2] **viXra:1311.0033 [pdf]**
*submitted on 2013-11-05 04:07:24*

**Authors:** Ralf Stephan

**Comments:** 2 Pages.

In this short note we give an expression for some numbers $n$ such that the polynomial $x^{2p}-nx^p+1$ is reducible.

**Category:** Number Theory

[1] **viXra:1311.0017 [pdf]**
*replaced on 2013-11-03 08:50:50*

**Authors:** Yibing Qiu

**Comments:** 1 Page.

This article redefine the prime number in angle with irreducible.

**Category:** Number Theory