[20] **viXra:1804.0291 [pdf]**
*submitted on 2018-04-20 19:53:17*

**Authors:** Sergey A. Lazarev

**Comments:** 4 Pages.

Prime number. Its nature, appearance, types, movement, prediction.

**Category:** Number Theory

[19] **viXra:1804.0289 [pdf]**
*submitted on 2018-04-20 22:09:15*

**Authors:** Walter Gress

**Comments:** 22 Pages.

A Sieve that extracts various properties of numerical sequences, demonstrating patterns in different types of sequences, rational, and irrational numbers.

**Category:** Number Theory

[18] **viXra:1804.0267 [pdf]**
*replaced on 2018-04-20 14:12:33*

**Authors:** John Atwell Moody

**Comments:** 8 Pages.

Let \alpha be the unique \Gamma(2) invariant form on H with a pole of residue -1 at i\infty and one of residue 1 at 1. Let \mu_{pm}:TxH->H be the action of multipying by \sqrt{g} and {1\over{\sqrt{g}} for g in the connected real multipplicative group T. For each real c in (0,1) and each unitary character \omega, the form g^{2-2c}\omega(g)\mu_+^*(\alpha+d\tau)\wedge \mu_-^*)\alpha+d\tau is exact if and only if \zeta(c+i\omega_0)=0 where \omega_0 is chosen such that \omega(g)=g^{i\omega_0}. The integral is equal to the stable distance from the origin in a dynamical system where a point is picked up and dropped off with two exponential rates. It spends time orbiting a fixed point or limit cycle before it is dropped off. It is only when c=1/2 that the two rates are equal.

**Category:** Number Theory

[17] **viXra:1804.0262 [pdf]**
*submitted on 2018-04-20 09:02:41*

**Authors:** Zeolla Gabriel Martín

**Comments:** 9 Pages.

The prime numbers greater than 5 have 4 terminations in their unit to infinity (1,3,7,9) and the composite numbers divisible by numbers greater than 3 have 5 terminations in their unit to infinity, these are (1,3,5,7,9). This paper develops an expression to calculate the prime numbers and composite numbers with ending 1.

**Category:** Number Theory

[16] **viXra:1804.0259 [pdf]**
*submitted on 2018-04-20 09:59:43*

**Authors:** M. A. Thomas

**Comments:** 3 Pages.

An observation of Diophantine sequences at or near the beginning of Prime sequences

**Category:** Number Theory

[15] **viXra:1804.0224 [pdf]**
*submitted on 2018-04-16 07:57:36*

**Authors:** Edgar Valdebenito

**Comments:** 4 Pages.

This note presents some formulas related with Malmsten's integral.

**Category:** Number Theory

[14] **viXra:1804.0223 [pdf]**
*submitted on 2018-04-16 07:59:39*

**Authors:** Edgar Valdebenito

**Comments:** 6 Pages.

This note presents some definite integrals.

**Category:** Number Theory

[13] **viXra:1804.0216 [pdf]**
*submitted on 2018-04-16 14:06:25*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2018 by Colin James III All rights reserved. info@cec-services dot com

The definition of the imaginary number is not tautologous and hence refuted.
The definition as rendered is contingent, the value for falsity.
While the definition can be coerced to be non-contingent, the value for truthity, it is still not tautologous.

**Category:** Number Theory

[12] **viXra:1804.0192 [pdf]**
*submitted on 2018-04-14 14:31:44*

**Authors:** Mendzina Essomba François

**Comments:** 10 Pages.

I propose in this article the first infinite products of history for inverse sinusoidal functions

**Category:** Number Theory

[11] **viXra:1804.0183 [pdf]**
*submitted on 2018-04-13 18:31:14*

**Authors:** Zeolla Gabriel Martín

**Comments:** 5 Pages.

This paper develops a modified an old and well-known expression for calculating and obtaining all twin prime numbers greater than three. The conditioning (n) will be the key to make the formula work.

**Category:** Number Theory

[10] **viXra:1804.0182 [pdf]**
*submitted on 2018-04-13 21:56:20*

**Authors:** Quang Nguyen Van

**Comments:** 4 Pages.

We give some quadratic formulas (including Euler's and Dirichlet's formula) of the equation X^(n-1) ∓ X^(n-2)Y + X^(n-3)Y^(n-2) ∓ … + Y^(n-1) = Z^n(nZ^n) in the cases n = 3, 5 and 7 for finding a solution in integer.

**Category:** Number Theory

[9] **viXra:1804.0052 [pdf]**
*submitted on 2018-04-03 07:58:59*

**Authors:** Raffaele Cogoni

**Comments:** 20 Pages. Testo di n° 20 pagine in lingua Italiana

Nel presente lavoro viene descritto un algoritmo per determinare la successione dei numeri primi, esso si presenta come una rielaborazione del noto Crivello di Eratostene.

**Category:** Number Theory

[8] **viXra:1804.0046 [pdf]**
*submitted on 2018-04-03 13:02:17*

**Authors:** Franco Sabino Stoianoff Lindstron

**Comments:** 2 Pages.

The method used in this article is based on analytical geometry, abstract algebra and number theory.

**Category:** Number Theory

[7] **viXra:1804.0039 [pdf]**
*submitted on 2018-04-02 15:49:23*

**Authors:** Franco Sabino Stoianoff Lindstron

**Comments:** 40 Pages.

The Beal Conjecture has been one of the most interesting problems that existed in number theory since the end of the last century. It was discovered by Andrew Beal during his work on Fermat's Last Theorem. In this paper a detailed review of the conjecture is proposed to end in a possible proof.

**Category:** Number Theory

[6] **viXra:1804.0038 [pdf]**
*replaced on 2018-04-11 21:14:55*

**Authors:** Philip Aaron Bloom

**Comments:** 3 Pages.

No simple proof of FLT has been established for every n >2 . To prove FLT we devise, for positive integral n, a detailed algebraic identity, r^n + s^n = t^n, that holds for positive real (r, s, t), which we can relate to x^n + y^n = z^n holding for positive integral (x, y, z). We show for n > 2 that there exists no positive integral (r, s, t). We infer that integral (r, s, t) equals integral (x, y, z) by using our identity's unrestricted variable. So, for n > 2, there exists no integral (x, y, z).

**Category:** Number Theory

[5] **viXra:1804.0037 [pdf]**
*submitted on 2018-04-02 16:53:15*

**Authors:** Zeolla Gabriel Martin

**Comments:** 4 Pages.

This paper shows that the product of the prime numbers adding and subtracting one is always Simple Prime numbers.

**Category:** Number Theory

[4] **viXra:1804.0036 [pdf]**
*replaced on 2018-04-12 23:10:20*

**Authors:** Radomir Majkic

**Comments:** 10 Pages. Apart from small technical and obvious language corrections, there is no difference between this and previously submitted version of the Goldbach’s Conjectures paper.

Abstract: The prime numbers set is the three primes addition closed; each prime is the sum of three not necessarily distinct primes. All natural numbers are created on the set of all prime numbers according to the laws of the weak and strong Goldbach's conjectures. Thus all natural numbers are the Goldbach's numbers.

**Category:** Number Theory

[3] **viXra:1804.0016 [pdf]**
*submitted on 2018-04-02 07:49:27*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

This note presents some formulas for Catalan's constant.

**Category:** Number Theory

[2] **viXra:1804.0008 [pdf]**
*submitted on 2018-04-02 12:49:21*

**Authors:** Victor Sorokine

**Comments:** 2 Pages.

Contradiction: Any prime factor r of the number R in the equality A n =A n +B n [...=(A+B)R]
has a single ending 0...01 of infinite length; where r≠n.
All calculations are done with numbers in base n, a prime number greater than 2.

**Category:** Number Theory

[1] **viXra:1804.0007 [pdf]**
*submitted on 2018-04-02 12:50:23*

**Authors:** Victor Sorokine

**Comments:** 2 Pages. Russian version

Contradiction: Any prime factor r of the number R in the equality A n =A n +B n [...=(A+B)R]
has a single ending 0...01 of infinite length; where r≠n.
All calculations are done with numbers in base n, a prime number greater than 2.
Противоречие: В равенстве A n =A n +B n [...=(A+B)R] любой простой сомножитель r (r≠n,
простое n>2) числа R имеет (в базе n) единичное окончание 0...01 бесконечной длины.
Все вычисления проводятся в системе счисления с простым основанием n>2.

**Category:** Number Theory