[48] **viXra:1910.0654 [pdf]**
*replaced on 2019-11-02 04:55:39*

**Authors:** Yuji Masuda

**Comments:** 1 Page.

This is a proof of Goldbach's conjecture.

**Category:** Number Theory

[47] **viXra:1910.0650 [pdf]**
*replaced on 2019-11-02 04:39:55*

**Authors:** Yuji Masuda

**Comments:** 1 Page.

This is proof of a famous formula.

**Category:** Number Theory

[46] **viXra:1910.0636 [pdf]**
*submitted on 2019-10-30 22:53:32*

**Authors:** Yuji Masuda

**Comments:** 1 Page.

This is collaboration3.

**Category:** Number Theory

[45] **viXra:1910.0634 [pdf]**
*submitted on 2019-10-30 00:30:29*

**Authors:** Yuji Masuda

**Comments:** 1 Page.

This is collaboration２.

**Category:** Number Theory

[44] **viXra:1910.0565 [pdf]**
*replaced on 2019-10-28 19:05:17*

**Authors:** Yuji Masuda

**Comments:** 1 Page.

This is collaboration.

**Category:** Number Theory

[43] **viXra:1910.0563 [pdf]**
*submitted on 2019-10-27 02:56:14*

**Authors:** Quang Nguyen Van

**Comments:** 3 Pages.

Adding to the known partial results, two famous Math problems : Beal conjecture and Fermat - Catalan conjecture are proved by one theorem -QS theorem that we propose in this article, and also means that the elementary proof of FLt has been found.

**Category:** Number Theory

[42] **viXra:1910.0558 [pdf]**
*submitted on 2019-10-27 07:27:30*

**Authors:** William F. Gilreath

**Comments:** 10 Pages. Published in the General Science Journal

Three fallacies that illustrate why division by zero is frequently considered undefined operation are examined. The example fallacies consider the unique case of zero divided by zero. Two examples are fallacies of equality, and the other is an example of ambiguity in the solution for an equation. These fallacies are examined using the transmathematic number nullity F. By utilizing nullity, division by zero is no longer an undefined or indeterminate operation, but a consistent, well-defined operation in arithmetic.

**Category:** Number Theory

[41] **viXra:1910.0551 [pdf]**
*replaced on 2019-10-30 02:26:02*

**Authors:** Timothy W. Jones

**Comments:** 4 Pages. A few corrections and improvements per some suggestions received.

With a strange and ironic twist an open number theory problem, show Zeta(n) is irrational for natural numbers greater than or equal to 2, is solved with the easiest of number theory concepts: the rules of representing fractions with decimals.

**Category:** Number Theory

[40] **viXra:1910.0549 [pdf]**
*submitted on 2019-10-26 17:08:03*

**Authors:** Michele Nardelli, Antonio Nardelli

**Comments:** 108 Pages.

In this research thesis, we have described some new mathematical connections between some equations of various topics concerning the Dilaton value, the D-Brane, the Bouncing Cosmology and some sectors of Number Theory (Riemann’s functions of S. Ramanujan and Rogers-Ramanujan continued fractions).

**Category:** Number Theory

[39] **viXra:1910.0538 [pdf]**
*submitted on 2019-10-26 07:33:48*

[38] **viXra:1910.0499 [pdf]**
*replaced on 2019-10-24 02:25:43*

[37] **viXra:1910.0494 [pdf]**
*submitted on 2019-10-24 05:10:18*

**Authors:** Zhiping Dai

**Comments:** 7 Pages.

Since the set of AS(+) and AS(×) is a bijective function, we use the improved the theorem of asymptotic density to prove that there exist prodcut of two odd primes in any AS(×).
At the same time, in any AS(+), the sum of two odd primes can be obtained.

**Category:** Number Theory

[36] **viXra:1910.0475 [pdf]**
*submitted on 2019-10-23 21:44:14*

**Authors:** Derek Tucker

**Comments:** 1 Page. Replaces the previous submission

Twin prime conjecture is proven from the observation that all composite odd numbers with factors greater than three occur in the cycle (0pm, 1pm, 5pm, 6pm), This draws circles with diameter 2p_m^2, and inter circle interval of 4p_m^2. For exclusively composite numbers we have |p_m^2±6p_m |.

**Category:** Number Theory

[35] **viXra:1910.0444 [pdf]**
*submitted on 2019-10-23 12:21:40*

**Authors:** Michele Nardelli, Antonio Nardelli

**Comments:** 152 Pages.

In this research thesis, we have described some new mathematical connections between some equations of the Ramanujan’s manuscripts, the Rogers-Ramanujan continued fractions and some sectors of Particle Physics (physical parameters of mesons and dilatons, in particular the values of the masses), String Theory and D-branes.

**Category:** Number Theory

[34] **viXra:1910.0411 [pdf]**
*submitted on 2019-10-21 03:47:35*

[33] **viXra:1910.0395 [pdf]**
*submitted on 2019-10-21 11:38:49*

**Authors:** Siddharth Bhatt

**Comments:** 1 Page.

When working with fractions, gravity always acts towards the division bar. This leads to a very non-intuitive result when yeeting a coefficient into the index. Since inverse yeeting is now done along the direction of gravity, the number itself gets inverted after reaching the index.

**Category:** Number Theory

[32] **viXra:1910.0367 [pdf]**
*submitted on 2019-10-20 11:45:58*

**Authors:** Derek Tucker

**Comments:** 3 Pages.

Proof of Legendre's conjecture by elementary means.

**Category:** Number Theory

[31] **viXra:1910.0366 [pdf]**
*submitted on 2019-10-20 11:58:01*

**Authors:** Abdelmajid Ben Hadj Salem

**Comments:** 53 Pages. Last version after correcting some topos errors. Submitted to the journal Compositio Mathematica.

In 1997, Andrew Beal announced the following conjecture: Let $A, B,C, m,n$, and $l$ be positive integers with $m,n,l > 2$. If $A^m + B^n = C^l$ then $A, B,$ and $C$ have a common factor. We begin to construct the polynomial $P(x)=(x-A^m)(x-B^n)(x+C^l)=x^3-px+q$ with $p,q$ integers depending of $A^m,B^n$ and $C^l$. We resolve $x^3-px+q=0$ and we obtain the three roots $x_1,x_2,x_3$ as functions of $p,q$ and a parameter $\theta$. Since $A^m,B^n,-C^l$ are the only roots of $x^3-px+q=0$, we discuss the conditions that $x_1,x_2,x_3$ are integers and have or not a common factor. Three numerical examples are given.

**Category:** Number Theory

[30] **viXra:1910.0365 [pdf]**
*submitted on 2019-10-20 11:57:05*

**Authors:** Derek Tucker

**Comments:** 1 Page.

Let y = exp(ln # - ln x) mod 1. The results show y = 0 for integer x if and only if x is a factor of #.

**Category:** Number Theory

[29] **viXra:1910.0364 [pdf]**
*submitted on 2019-10-19 15:17:19*

**Authors:** Michele Nardelli, Antonio Nardelli

**Comments:** 59 Pages.

In this research thesis, we have described some new mathematical connections between some equations of various sectors concerning the D-Branes and some Ramanujan’s modular equations and approximations to π.

**Category:** Number Theory

[28] **viXra:1910.0349 [pdf]**
*replaced on 2019-11-04 03:39:57*

**Authors:** Y.Mieno

**Comments:** 5 Pages.

A few progressions of the same type and their periodic sequences.

**Category:** Number Theory

[27] **viXra:1910.0322 [pdf]**
*submitted on 2019-10-18 12:33:20*

**Authors:** Michele Nardelli, Antonio Nardelli

**Comments:** 201 Pages.

In this research thesis, we have described some new mathematical connections between some equations of various topics concerning the D-Branes and some sectors of Number Theory (Rogers-Ramanujan continued fractions and mock theta functions).

**Category:** Number Theory

[26] **viXra:1910.0317 [pdf]**
*submitted on 2019-10-17 02:18:31*

**Authors:** Wu Ye TangYin

**Comments:** 13 Pages. Please forgive me for my low level of mathematics writing. The article is right

According to the random theory and hypothesis theory, the calculation of any number is pushed to infinity. In this paper, 2n-a = 2 * B (B does not know whether it is prime number, or compound number. So the hypothesis plays an important role in judgment. If B is equal to prime, then there is no need to calculate. If B is a compound number, its factorization prime factor, we can get the prime number, and then we can calculate it. But infinity belongs to the unknown.
We don't know what it is to decompose prime factors. Only a, B, C, D.. Then suppose it is a composite number. In this paper, it is only for infinite odd numbers. Is there an inverse column? Odd numbers are not equal to two same prime numbers, plus the sum of odd prime numbers.)

**Category:** Number Theory

[25] **viXra:1910.0316 [pdf]**
*submitted on 2019-10-17 02:46:52*

**Authors:** Wu Ye TangYin

**Comments:** 13 Pages. Who is willing to help me revise the article? My writing level is low. But theoretical logic is right. Help me get in touch with math magazines.

o prove the idea, assuming that any even number can not be equal to the sum of two prime numbers, then according to the analog computing logic.
Subject: Use hypothesis to judge unknown. In infinite even numbers, there are only numbers, a, b, c, D. Can only be judged; it's prime, or compound.
When: 2N－P=B (B, it is a prime number, or it is a compound number), the hypothesis is used as the basis of judgment. If B equals a prime number, there is no need to calculate it. But B is an unknown number. Judge it to be a prime or a compound number. Assuming a complex number, it can decompose the prime factor. We can get prime numbers. Here, we use hypothesis computing theory to push the unknown to infinity.。Find any even number, there are prime pairs.（Abbreviation：2N=Pa＋Pb）

**Category:** Number Theory

[24] **viXra:1910.0281 [pdf]**
*replaced on 2019-12-29 20:29:20*

**Authors:** Felix M. Lev

**Comments:** 11 Pages.

The {\it technique} of classical mathematics involves only potential infinity, i.e. infinity is understood only as a limit, and, as a rule, legitimacy of every limit is thoroughly investigated. However, {\it the basis} of classical mathematics does involve actual infinity: the infinite ring of integers $Z$ is the starting point for constructing infinite sets with different cardinalities, and, even in standard textbooks on classical mathematics, it is not even posed a problem whether $Z$ can be treated as a limit of finite sets. On the other hand, finite mathematics starts from the ring $R_p=(0,1,...p-1)$ (where all operations are modulo $p$) and the theory deals only with a finite number of elements. We give a direct proof that $Z$ can be treated as a limit of $R_p$ when $p\to\infty$, and the proof does not involve actual infinity. Then we explain that, as a consequence, finite mathematics is more fundamental than classical one.

**Category:** Number Theory

[23] **viXra:1910.0261 [pdf]**
*submitted on 2019-10-15 19:05:23*

**Authors:** Derek Tucker

**Comments:** 7 Pages.

Our objective is to demistify prime gaps in the integers. We will show that the explicit range of prime gaps in the integers is bounded from below by two and above by the expression 〖2p〗_(n-1) , valid for gaps beginning 〖(p〗_n^2-1)-p_(n-1). This upper bound theoretically becomes necessarily greater than empirical observation within empirically verified range, enabling explicit closure on prime gap issues. These results confirm the prime pattens conjecture and the Prime Inter-Square Conjecture (PISC) Legendre’s conjecture.

**Category:** Number Theory

[22] **viXra:1910.0239 [pdf]**
*submitted on 2019-10-14 16:47:14*

**Authors:** Mesut Kavak

**Comments:** 3 Pages.

While I was working about some basic physical phenomena, I discovered some geometric relations that also interest mathematics. In this work, I applied the rules I have been proven to P=NP? problem over impossibility of perpendicularity in the universe. It also brings out extremely interesting results out like imaginary numbers which are known as real numbers currently. Also it seems that Euclidean Geometry is impossible. The actual geometry is Riemann Geometry and complex numbers are real.

**Category:** Number Theory

[21] **viXra:1910.0237 [pdf]**
*submitted on 2019-10-14 22:04:42*

[20] **viXra:1910.0201 [pdf]**
*submitted on 2019-10-12 14:31:09*

**Authors:** Michele Nardelli, Antonio Nardelli

**Comments:** 113 Pages.

In this research thesis, we have described some new mathematical connections between some equations of Dirichlet L-functions, some equations of D-Branes and Rogers-Ramanujan continued fractions.

**Category:** Number Theory

[19] **viXra:1910.0182 [pdf]**
*submitted on 2019-10-11 22:27:52*

**Authors:** Yuji Masuda

**Comments:** 1 Page.

I was suprised.

**Category:** Number Theory

[18] **viXra:1910.0180 [pdf]**
*submitted on 2019-10-11 02:45:25*

**Authors:** Pedro Hugo García Peláez

**Comments:** 4 Pages.

Factorization of the numbers of the form n + n ^ 2 it can be done with a certain algorithm.

**Category:** Number Theory

[17] **viXra:1910.0179 [pdf]**
*submitted on 2019-10-11 02:53:16*

**Authors:** Pedro Hugo García Peláez

**Comments:** 4 Pages.

Los números de la forma n+n^2 se pueden factorizar con un cierto algoritmo.

**Category:** Number Theory

[16] **viXra:1910.0167 [pdf]**
*submitted on 2019-10-10 16:25:26*

**Authors:** Colin James III

**Comments:** 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Note that Disqus comments here are not read by the author; reply by email only to: info@cec-services dot com. Include a list publications for veracity. Updated abstract at ersatz-systems.com.

We evaluate the definition of the Goldbach succession gap (GSG) as not tautologous and contradictory. This means that if the fact of each gap of zero order in a GSG as the difference of squares is based on a contradiction, then Goldbach's strong conjecture and twin primes conjecture are also refuted. Initial proof of the theorem of succession by the inference of induction weakens further the arrival at a definition of GSG . These results form a non tautologous fragment of the universal logic VŁ4.

**Category:** Number Theory

[15] **viXra:1910.0157 [pdf]**
*submitted on 2019-10-10 07:42:33*

**Authors:** Michele Nardelli, Antonio Nardelli

**Comments:** 308 Pages.

In this research thesis, we have described some new mathematical connections between some equations of certain Dirichlet series, some equations of D-Branes and Rogers-Ramanujan formulas that link π, e and ϕ.

**Category:** Number Theory

[14] **viXra:1910.0142 [pdf]**
*submitted on 2019-10-09 07:17:22*

**Authors:** Horacio useche losada

**Comments:** 25 Pages. Primer millón de números primos calculados con una fórmula para el n-ésimo primo

Conseguir una fórmula, un procedimiento o algoritmo para computar el n-
ésimo primo, ha sido siempre un viejo anhelo de los matemáticos. Sin em-
bargo, en la literatura cientı́fica solo se reportan fórmulas basadas en el teo-
rema de Wilson, las cuales, carecen de un valor práctico y solo pueden tener
un interés estrictamente teórico, ya que no se puede llegar muy lejos al in-
tentar su uso en cálculos concretos.
Esta investigación retoma un trabajo del profesor Ramón Fandiño,1 el
cual, presenta en 1980 una relación funcional a partir de la cual se puede com-
putar el n-ésimo primo en función de los n − 1 primos anteriores. Para con-
seguir el objetivo, el profesor Fandiño realiza cinco ajustes, tres por mı́nimos
cuadrados y dos por técnicas implementadas por él mismo, con lo cual con-
sigue calcular los primeros 5000 primos.
Siguiendo la lı́nea de investigación del citado profesor, pero haciendo al-
gunos cambios importantes en el modelo matemático usado y con un menor
número de ajustes, he conseguido computar un millón de números pri-
mos, advirtiendo que es posible computar muchos más,2 si se cuenta con
las herramientas de hardware adecuadas. En esta ocasión, he usado un PC
casero3 , una máquina corriente que logró computar dicha cantidad en tan solo
una hora y 21 minutos! Para hacernos una idea del esfuerzo computacional,
en su momento el profesor Fandiño utilizó, no un PC, sino un computador
de verdad, un IBM 360/44 que era la máquina más poderosa del centro de
cómputo de la UN (y posiblemente de Colombia).4
Con un “juguete”de cómputo, me complace presentar esta cifra que se
enmarca en una polı́tica denominada “resultados sorprendentes con recursos
mediocres”tal y como acontece con otros trabajos de este autor (ver [5], [6], y
[7]). Espero muy pronto superar esta cifra usando un hardware más poderoso,
naturalmente.

**Category:** Number Theory

[13] **viXra:1910.0137 [pdf]**
*submitted on 2019-10-09 10:09:21*

**Authors:** Miguel Cerdá Bennassar

**Comments:** 35 Pages.

Abstract: I propose a numerical table that demonstrates visually that the sequences formed with Collatz's algorithm always reach 1.

**Category:** Number Theory

[12] **viXra:1910.0129 [pdf]**
*submitted on 2019-10-09 02:07:26*

[11] **viXra:1910.0128 [pdf]**
*submitted on 2019-10-08 19:35:03*

**Authors:** Colin James III

**Comments:** 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Note that Disqus comments here are not read by the author; reply by email only to: info@cec-services dot com. Include a list publications for veracity. Updated abstract at ersatz-systems.com.

We evaluate Wüsthofen’s conjecture and counter-example in the title, Benzmüller’s confirmation of Wüsthofen’s conjecture, and Benzmüller’s counter model to Wüsthofen’s counter-example: all four are not tautologous. The claim that the paper in LaTex extension of the proof assistant Isabelle/HOL constitutes a verified proof document is also refuted. These results form a non tautologous fragment of the universal logic VŁ4.

**Category:** Number Theory

[10] **viXra:1910.0120 [pdf]**
*submitted on 2019-10-08 00:06:45*

**Authors:** Yuji Masuda

**Comments:** 23 Pages.

This is on primes⑦

**Category:** Number Theory

[9] **viXra:1910.0117 [pdf]**
*submitted on 2019-10-08 06:37:37*

**Authors:** Michele Nardelli, Antonio Nardelli

**Comments:** 153 Pages.

In this research thesis, we have described some new mathematical connections between some equations of certain Dirichlet series, some equations of D-Branes and Rogers-Ramanujan formulas that link π, e and ϕ.

**Category:** Number Theory

[8] **viXra:1910.0116 [pdf]**
*submitted on 2019-10-08 06:50:03*

**Authors:** Suraj Deshmukh

**Comments:** 7 Pages.

In This paper we will use a simple Logo software to demonstrate a possible
pattern in prime numbers. We Will see how primes show a tendency to retrace the
path of other primes.

**Category:** Number Theory

[7] **viXra:1910.0115 [pdf]**
*submitted on 2019-10-08 07:07:54*

**Authors:** David Streit, Christoph Benzmüller

**Comments:** 12 Pages.

The present paper is a technical report on 'The Inconsistency of Arithmetic' available on http://vixra.org/abs/1904.0428. It contains a formalized analysis where the authors claim to "constitute a veriﬁed proof document" by an automated verification using the proof assistant 'Isabelle / HOL'. In order to refute the key statement (II) on page 2 of the inconsistency proof, the authors seek to create a countermodel. However, this model is based on an erroneous application of predicate logic. The crucial point is the lemma on page 7 which is proved wrongly. For that statement becoming true, the two sets S1, S2 have to exist for the case that (G) is true and for the case that (G) is false, and not the other way around: if (G) is true there is a pair of unequal sets that does the job and if (G) is false there is another pair.

**Category:** Number Theory

[6] **viXra:1910.0105 [pdf]**
*replaced on 2019-10-08 11:41:30*

**Authors:** Bassam Abdul-Baki

**Comments:** 31 Pages.

The minimal set for powers of 2 is currently nondeterministic and can be shown to be more complex than previously proposed.

**Category:** Number Theory

[5] **viXra:1910.0081 [pdf]**
*replaced on 2019-11-26 18:47:27*

**Authors:** Toshiro Takami

**Comments:** 10 Pages.

I proved the Twin Prime Conjecture.
All Twin Primes are executed in hexadecimal notation. It does not change in a huge number (forever huge number).
In the hexagon, prime numbers are generated only at [6n -1] [6n+1]. (n is a positive integer)
The probability that a twin prime will occur is 6/5 times the square of the probability that a prime will occur.
If the number is very large, the probability of generating a prime number is low, but since the prime number exists forever, the probability of generating a twin prime number is very low, but a twin prime number is produced.
That is, twin primes exist forever.

**Category:** Number Theory

[4] **viXra:1910.0077 [pdf]**
*submitted on 2019-10-05 23:10:40*

**Authors:** Radomir Majkic

**Comments:** 3 Pages. The author's name typing error s corrected.

The collection of the consecutive composite integers is the composite connected, and no pair of its distinct integers may be generated by a single prime number.
Consequently, it is possible to select at least one collection of distinct prime divisors by extracting only one prime from every single integer of the collection, and the Grimm's Conjecture holds.

**Category:** Number Theory

[3] **viXra:1910.0075 [pdf]**
*submitted on 2019-10-06 03:14:06*

**Authors:** Ilija Barukčić

**Comments:** 6 pages. Copyright © 2019 by Ilija Barukčić, Jever, Germany. All rights reserved. Published by:

Objective: The division 0/0 has been investigated by numerous publications while the knowledge that 0/0 = 1 is still not established yet.
Methods: A systematic re-analysis of the claim (0/0) = 0 was conducted again. Modus inversus was used to proof the logical consistency of such a claim.
Results: The new proof provides strict evidence that 0/0=0 is not correct.
Conclusions: 0/0=0 is refuted.
Keywords: Division by zero, Modus inversus.

**Category:** Number Theory

[2] **viXra:1910.0021 [pdf]**
*submitted on 2019-10-01 15:27:10*

**Authors:** Michele Nardelli, Antonio Nardelli

**Comments:** 210 Pages.

In the present research thesis, we have obtained various and interesting new possible mathematical results concerning the Rogers-Ramanujan identities and some continued fractions. Furthermore, we have described new possible mathematical connections with the mass value of candidate “glueball” f0(1710) meson, other particles and with the Black Hole entropies.

**Category:** Number Theory

[1] **viXra:1910.0017 [pdf]**
*replaced on 2019-10-02 05:02:19*