[29] **viXra:1804.0492 [pdf]**
*submitted on 2018-04-30 18:32:49*

**Authors:** Nazihkhelifa

**Comments:** 1 Page. Version 1

Prime Number Formula

**Category:** Number Theory

[28] **viXra:1804.0474 [pdf]**
*submitted on 2018-04-28 14:33:16*

**Authors:** Elizabeth Gatton-Robey

**Comments:** 2 Pages.

I created an algorithm that guarantees the validity of Goldbach’s Conjecture.
The algorithm eliminates all even integers that are not the sum of an even integer when the number 3 is added to one other prime number.
The visual pattern that emerges from the algorithm maps all prime numbers. This pattern is also applied to individual consecutive primes to eliminate all even numbers that are not the sum of each prime number plus one other prime number.
By layering the pattern to account for all possible “sums of two prime numbers” combinations, it can either be said that “all evens will be eliminated” or “no evens will be eliminated”. What this means is that what happens to one even integer is universal.

**Category:** Number Theory

[27] **viXra:1804.0470 [pdf]**
*submitted on 2018-04-28 18:44:49*

**Authors:** Colin James III

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

The distribution is confirmed as random and refuted as not clumped as in claims by various theoretical methods.

**Category:** Number Theory

[26] **viXra:1804.0416 [pdf]**
*replaced on 2018-07-02 20:34:06*

**Authors:** Waldemar Puszkarz

**Comments:** 7 Pages. Last version submitted to viXra. First version submitted to arXiv.

Computer experiments reveal that twin primes tend to center on nonsquarefree multiples of 6 more often than on squarefree multiples of 6 compared to what should be expected from the ratio of the number of nonsquarefree multiples of 6 to the number of squarefree multiples of 6 equal $\pi^2/3-1$, or ca 2.290. For multiples of 6 surrounded by twin primes, this ratio is 2.427, a relative difference of ca $6.0\%$ measured against the expected value. A deviation from the expected value of this ratio, ca $1.9\%$, exists also for isolated primes. This shows that the distribution of primes is biased towards nonsquarefree numbers, a phenomenon most likely previously unknown. For twins, this leads to nonsquarefree numbers gaining an excess of $1.2\%$ of the total number of twins. In the case of isolated primes, this excess for nonsquarefree numbers amounts to $0.4\%$ of the total number of such primes. The above numbers are for the first $10^{10}$ primes, with the bias showing a tendency to grow, at least for isolated primes.

**Category:** Number Theory

[25] **viXra:1804.0409 [pdf]**
*replaced on 2018-06-27 04:06:28*

**Authors:** Andrey B. Skrypnik

**Comments:** 4 Pages.

Now there is a formula for calculating all primes

**Category:** Number Theory

[24] **viXra:1804.0385 [pdf]**
*submitted on 2018-04-25 21:32:26*

**Authors:** Bing He, Hongcun Zhai

**Comments:** 7 Pages. This is a joint work with Dr. Zhai.

From a very-well-poised _{6}\phi_{5} series formula we deduce a general series expansion formula involving the q-gamma function.
With this formula we can give q-analogues of many Ramanujan-type series.

**Category:** Number Theory

[23] **viXra:1804.0376 [pdf]**
*submitted on 2018-04-26 06:38:20*

**Authors:** Angel Garcés Doz

**Comments:** 9 Pages.

This modest article shows the connection between the strong Goldbach conjecture and the topological properties of the Klein bottle and the Möbius strip. This connection is established by functions derived from the number of divisors of the two odd integers whose sum is an even number.

**Category:** Number Theory

[22] **viXra:1804.0366 [pdf]**
*submitted on 2018-04-24 16:44:53*

**Authors:** H.L. Mitchell

**Comments:** 12 Pages.

We introduce a sieve for the number of twin primes less than n by sieving through the set {k ∊ ℤ+ | 6k < n}. We derive formula accordingly using the Euler product and the Brun Sieve.
We then use the Prime Number Theorem and Mertens’ Theorem.
The main results are:
1) A sieve for the twin primes similar to the sieve of Eratosthenes for primes involving only the
values of k, the indices of the multiples of 6, ranging over k = p ,5 ≤ p <√n.It shows the uniform
distribution of the pairs (6k-1,6k+1) that are not twin primes and the decreasing frequency of
multiples of p as p increases.
2) A formula for the approximate number of twin primes less than N in terms of the number of
primes less than n
3) The asymptotic formula for the number of twin primes less than n verifying the Hardy
Littlewood Conjecture.

**Category:** Number Theory

[21] **viXra:1804.0337 [pdf]**
*submitted on 2018-04-23 23:50:14*

**Authors:** Walter Gress

**Comments:** 12 Pages.

This work expounds upon a theory of peripheral-integers and peripheral-reals, integers and reals that in a modular number line mirror their counterparts. It illustrates the properties of these numbers in hopes to breathe life into research of numbers that go beyond infinity

**Category:** Number Theory

[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 2018-06-06 04:30:05*

**Authors:** John Atwell Moody

**Comments:** 14 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. The ratio [\alpha: i\pi dtau] tends to 1 at the upper limit of [0,i\infty). Let \mu_{pm}:TxH->H be the action of multiplying by \sqrt{g} and {1\over{\sqrt{g}} for g in the connected real multiplicative group T. For each real c in (0,1) and each unitary character \omega, the form g^{2-2c}\omega(g)\mu_+^*(\alpha-\pi d\tau)\wedge \mu_-^*)\alpha-i\pi 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 rate of change of the magnitude is given by an integral involving a unitary character. Conjecturally the rate seminegative on the region 0
The form descends to the real projective line, it is locally meromorphic there with one pole and integrates to \pi e^{i\pi ({3\over 2}s + 1}. The value \zeta(s)=0 if and only if the integral along the arc from 0 to \infty not passing 1 is zero. This implies the arc passing through 1 equals a residue. We begin to relate the equality with the condition Re(s)=1/2.

**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]**
*replaced on 2018-05-21 14:45:07*

**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 2018-05-16 17:09:45*

**Authors:** Philip Aaron Bloom

**Comments:** 3 Pages.

No simple proof of FLT has been established for every n > 2. We devise, for positive integral values of n, an elaborate algebraic identity, r^n + s^n = t^n, that holds for positive integral (r, s, t), a triple that we relate to positive integral (x, y, z) for which x^n + y^n = z^n holds. We infer that integral (r, s, t) equals integral (x, y, z) by using the unrestricted variable in our identity. For n > 2, we demonstrate that there exists no integral (r, s, t). Hence, 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