[16] **viXra:1411.0579 [pdf]**
*submitted on 2014-11-27 09:52:30*

**Authors:** Prashanth R. Rao

**Comments:** 2 Pages.

In a previous paper we derived that if p, p+2 are twin-primes then
2^{p-2} is of the form (pz+y) where z, y must have unique solutions. We extend this result to derive a single criterion that we believe is novel that may be useful to screen for candidate twin primes.

**Category:** Number Theory

[15] **viXra:1411.0571 [pdf]**
*submitted on 2014-11-27 03:35:47*

**Authors:** Marius Coman

**Comments:** 4 Pages.

In this paper I define few formulas which conduct from any odd prime respectively from any pair of distinct odd primes to an infinity of probably infinite sequences of primes, also to such sequences of a certain kind of semiprimes, and I also make a generalization of a Cunningham chain of primes of the first kind, respectively of the second kind.

**Category:** Number Theory

[14] **viXra:1411.0569 [pdf]**
*submitted on 2014-11-26 09:36:47*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make a conjecture which states that there exist an infinity of primes of the form N/3^m, where m is positive integer and N is the number formed concatenating to the left a Carmichael number with the number 584. Such primes are 649081 = 5841729/3^2, 1947607 = 5842821/3, 1948867 = 5846601/3 etc. I also make few comments about a certain kind of semiprimes.

**Category:** Number Theory

[13] **viXra:1411.0545 [pdf]**
*submitted on 2014-11-22 21:46:43*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make a conjecture which states that from any two odd primes p1 and p2 can be obtained, through an iterative and very simple operation, a prime p3 larger than p1 and also larger than p2.

**Category:** Number Theory

[12] **viXra:1411.0539 [pdf]**
*submitted on 2014-11-22 08:38:35*

**Authors:** Maik Becker-Sievert

**Comments:** 1 Page.

Formula to generate all Pythagorean Triple

**Category:** Number Theory

[11] **viXra:1411.0537 [pdf]**
*submitted on 2014-11-22 04:45:28*

**Authors:** Maik Becker-Sievert

**Comments:** 1 Page.

Pythagorean Triple Formulas

**Category:** Number Theory

[10] **viXra:1411.0481 [pdf]**
*submitted on 2014-11-20 14:02:24*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make few observations on a class of Smarandache generalized Fermat numbers, which are the numbers of the form F(k) = a^(b^k) + c, where a, b are integers greater than or equal to 2 and c is integer such that (a, c) = 1. The class that is observed in this paper includes the numbers of the form F(k) = m^(n^k) + n, where k is positive integer and m and n are coprime positive integers, not both of them odd or both of them even.

**Category:** Number Theory

[9] **viXra:1411.0436 [pdf]**
*replaced on 2014-11-20 13:26:16*

**Authors:** Marius Coman

**Comments:** 3 Pages.

In this paper I make few conjectures on few classes of generalized Fermat numbers, i.e. the numbers of the form F(k) = 2^(2^k) + n, where k is positive integer and n is an odd number, the numbers of the form F(k) = 4^(4^k) + 3 and the numbers of the form F(k) = m^(m^k) + n, where m + n = p, where p is prime, all subclasses of Smarandache generalized Fermat numbers, i.e. the numbers of the form F(k) = a^(b^k) + c, where a, b are integers greater than or equal to 2 and c is integer such that (a, c) = 1.

**Category:** Number Theory

[8] **viXra:1411.0109 [pdf]**
*replaced on 2014-11-14 07:38:24*

**Authors:** A. Garcés Doz

**Comments:** 9 Pages. Corrected a mistake that does not affect at all the proof

In this study we propose a demonstration of the impossibility of odd perfect numbers.This proof uses a congruence, which is implicit in the condition, mandatory, demonstrated by Euler. More precisely, a congruence that must be fulfilled in the equation that equals the number 2N, with Euler condition, and the formula for the sum of the divisors of the odd number N. Following a rigorous and meticulous way, this mandatory congruence; a final equation is obtained after one polynomial simplification on both sides of the original equation that equals the number 2N with the sum of the divisors of the number N. With this final equation, the impossibility of the existence of odd perfect numbers is demonstrated by applying several lemmas.These lemmas are demonstrations already established by W. Ljunggren, Maohua Le, Nagell, among others. With a lemma that establishes mandatory requirements, and two other lemmas for the absence of solutions on certain specific Diophantine equations ( (x^n - 1)/(x-1) = y^2 ; (x^n + 1)/(x+1) = y^2 ; n = 2z + 1); ultimately lead to the demonstration of the nonexistence of odd perfect numbers.

**Category:** Number Theory

[7] **viXra:1411.0084 [pdf]**
*submitted on 2014-11-10 11:32:55*

**Authors:** Th.G.

**Comments:** 1 Page.

Why the ABC-Conjecture never holds
by
tom.gu8@gmail.com

**Category:** Number Theory

[6] **viXra:1411.0075 [pdf]**
*submitted on 2014-11-08 23:05:43*

**Authors:** A. A. Frempong

**Comments:** 9 Pages. Copyright © A. A. Frempong

Assuming the sum of the original Riemann series is L, a ratio method was used to split-up the series equation into sub-equations and each sub-equation was solved in terms of L, and ratio terms. It is to be noted that unquestionably, each term of the series equation contributes to the sum, L, of the series. There are infinitely many sub-equations and solutions corresponding to the infinitely many terms of the series equation. After the sum, L, and the ratio terms have been determined and substituted in the corresponding equations, the Riemann hypothesis would surely be either proved or disproved, since the original equation is being solved. Using the original series equation eliminates possible hidden flaws in derived equations and consequent solutions.

**Category:** Number Theory

[5] **viXra:1411.0071 [pdf]**
*submitted on 2014-11-08 14:46:15*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I present a formula, based on the numbers 7 and 186, that, using primes as input values, often leads, as output values, to larger primes, also to squares of primes and semiprimes. I found this formula by chance, playing with two of my favourite numbers, 13 and 31, and observing that 7*13^2 + 6*31 = 37^2 (to be noted, without necessarily connection with this paper, that the difference between the two known Wieferich primes, 1093 and 3511, is equal to 6*13*31).

**Category:** Number Theory

[4] **viXra:1411.0069 [pdf]**
*submitted on 2014-11-08 11:54:38*

**Authors:** Marius Coman

**Comments:** 3 Pages.

In one of my previous papers, “A possible infinite subset of Poulet numbers generated by a formula based on Wieferich primes” I pointed an interesting relation between Poulet numbers and the two known Wieferich primes (not the known fact that the squares of these two primes are Poulet numbers themselves but a way to relate an entire set of Poulet numbers by a Wieferich prime). Exploring further that formula I found a way to generate primes, respectively semiprimes of the form q1*q2, where q2 – q1 is equal to a multiple of 30.

**Category:** Number Theory

[3] **viXra:1411.0065 [pdf]**
*submitted on 2014-11-07 17:04:01*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I combine my interest for Carmichael numbers with my interest for finding formulas that generate large primes or products of very few primes showing few easy ways for obtaining such numbers and at the same time an interesting relation between absolute Fermat pseudoprimes and the number 375.

**Category:** Number Theory

[2] **viXra:1411.0020 [pdf]**
*replaced on 2014-11-07 15:24:10*

**Authors:** Marius Coman

**Comments:** 5 Pages.

In one of my previous papers, namely “A conjecture about a large subset of Carmichael numbers related to concatenation”, I obtained interesting results combining the method of deconcatenation with the method of congruence modulo. Applying the same methods to the prime factors of the Fibonacci numbers I found also notable patterns.

**Category:** Number Theory

[1] **viXra:1411.0011 [pdf]**
*replaced on 2014-11-07 01:30:46*

**Authors:** T.Nakashima

**Comments:** 2 Pages.

A doubt of the classialy well known proof.

**Category:** Number Theory