[21] **viXra:1903.0553 [pdf]**
*submitted on 2019-03-30 08:25:45*

**Authors:** Daoudi Rédoane

**Comments:** 1 Page.

Here I present one formula that produces prime numbers. There are counterexamples for this formula.

**Category:** Number Theory

[20] **viXra:1903.0548 [pdf]**
*replaced on 2019-04-15 08:36:19*

**Authors:** Ilija Barukčić

**Comments:** 18 Pages.

Abstract
Objectives:
The scientific knowledge appears to grow by time. However, every scientific progress involves different kind of mistakes, which may survive for a long time. Nevertheless, the abandonment of partially true or falsified theorems, theories et cetera, for positions which approach more closely to the truth, is necessary. In a critical sense, a reduction of the myth in science demands the non-ending detection of contradictions in science and the elimination the same too.
Methods:
Nullity as one aspect of the trans-real arithmetic and equally as one of today’s approaches to the solution of the problem of the division of zero by zero is re-analyzed. A systematic mathematical proof is provided to prove the logical consistency of Nullity.
Results:
There is convincing evidence that Nullity is logically inconsistent. Furthermore, the about 2000 year old rule of the addition of zero’s (0+0+…+0 = 0) is proved as logically inconsistent and refuted.
Conclusion: Nullity is self-contradictory and refuted.
Keywords: Indeterminate forms, Classical logic, Zero divided by zero

**Category:** Number Theory

[19] **viXra:1903.0543 [pdf]**
*submitted on 2019-03-31 01:17:07*

**Authors:** Faisal Amin Yassein Abdelmohssin

**Comments:** 2 Pages.

I give definition of Beautiful Natural Numbers (BNNs) and relate it to the theorem I claimed earlier on distinct proper fractions that sum to 1.

**Category:** Number Theory

[18] **viXra:1903.0503 [pdf]**
*replaced on 2019-04-17 03:51:24*

**Authors:** Timothy W. Jones

**Comments:** 16 Pages. A new section that shows with greater clarity the extension of Sondow has been added.

We modify Sondow's geometric proof of the irrationality of e. The modification uses sector areas on circles, rather than closed intervals. Using this circular version of Sondow's proof, we see a way to understand the irrationality of a series. We evolve the idea of proving all possible rational value convergence points of a series are excluded because all partials are not expressible as fractions with the denominators of their terms. If such fractions cover the rationals, then the series should be irrational. Both the irrationality of e and that of zeta(n>=2) are proven using these criteria: the terms cover the rationals and the partials escape the terms.

**Category:** Number Theory

[17] **viXra:1903.0483 [pdf]**
*replaced on 2019-05-31 03:36:02*

**Authors:** John Yuk Ching Ting

**Comments:** 20 Pages. Rigorous proof for Riemann hypothesis and explaining Gram points.

Riemann hypothesis proposed all nontrivial zeros to be located on critical line of Riemann zeta function. Treated as Incompletely Predictable problem, we obtain Dirichlet Sigma-Power Law as final proof of solving this problem. This Law is derived as equation and inequation from original Dirichlet eta function (proxy function for Riemann zeta function). Performing a parallel procedure help explain closely related Gram points.

**Category:** Number Theory

[16] **viXra:1903.0464 [pdf]**
*replaced on 2019-03-28 08:32:43*

**Authors:** Ilija Barukčić

**Comments:** 5 Pages. Copyright © 2019 by Ilija Baruk�?ić, Jever, Germany. All rights reserved. Published by: Ilija Baruk�?ić "The Interior Logic of Inequalities" IJMTT, 65 (7) (2019): 146-155. doi: 10.14445/22315373/IJMTT-V65I7P524

Saitho’s equality (1/0)=(0/0) is self-contradictory and refuted.

**Category:** Number Theory

[15] **viXra:1903.0439 [pdf]**
*submitted on 2019-03-24 07:13:24*

**Authors:** Yuly Shipilevsky

**Comments:** 7 Pages.

We introduce a special class of complex numbers, wherein their
absolute values and arguments given in a polar coordinate system are integers
and we introduce the corresponding class of the Optimization Problems:
"Polar Complex Integer Optimization

**Category:** Number Theory

[14] **viXra:1903.0390 [pdf]**
*submitted on 2019-03-21 22:53:24*

**Authors:** Soerivhe Iriene, J. Oquibo Ihwaiuwaue

**Comments:** 6 Pages.

The paper "Proof of the Polignac Prime Conjecture and other Conjectures", (although listed under the title "Elementary Proof of the Goldbach Conjecture") first published in 2017 claimed to have proven Polignac's conjecture, and in doing so also the twin prime conjecture. The said paper had several problems, not least of which was a catastrophic basic error that completely invalidated the proof. Polignac's conjecture remains unproven, as does the twin primes conjecture.

**Category:** Number Theory

[13] **viXra:1903.0387 [pdf]**
*replaced on 2019-03-22 08:40:24*

**Authors:** Juan Moreno Borrallo

**Comments:** 7 Pages. Spanish Language

At this brief paper, it is proposed and demonstrated a curious identity of Zeta Function, equivalent to the sum of the geometric progression of reciprocals of all the positive integers which are not perfect powers, having as numerators the number of divisors of the exponent of each term of the progression.

**Category:** Number Theory

[12] **viXra:1903.0353 [pdf]**
*replaced on 2019-04-18 21:47:07*

**Authors:** Sally Myers Moite

**Comments:** 9 Pages.

Numbers of form 6N – 1 and 6N + 1 factor into numbers of the same form. This observation provides elimination sieves for numbers N that lead to primes and prime pairs. The sieves do not explicitly reference primes.

**Category:** Number Theory

[11] **viXra:1903.0333 [pdf]**
*replaced on 2019-11-05 16:31:14*

**Authors:** Toshiro Takami

**Comments:** 134 Pages.

I also found a zero point which seems to deviate from 0.5.
I thought that the zero point outside 0.5 can not be found very easily in the area which can not be shown in the figure, but this area can not be represented in the figure but can be found one after another.
It is completely unknown whether this axis is distorted in the 0.5 axis or just by coincidence.
The number of zero points in the area that can not be shown in the figure is now 43.
No matter how you looked it was not found in other areas.
It seemed that there is no other way to interpret this axis as 0.5 axis is distorted in this area.
Somewhere on the net there is a memory that reads the mathematician's view that
"there are countless zero points in the vicinity of 0.5 on high area".
We are reporting that the zero point search of the high-value area of the imaginary part which was giving up as it is no longer possible with the supercomputer is no longer possible, is reported.
43 zero-point searches in the high-value area of the imaginary part are thus successful.
This means that the zero point search in the high-value area of the imaginary part has succeeded in the 43.
We will also write 43 zero point searches of the successful high-value area of the imaginary part.
There are many counterexamples far beyond 0.5, which is far beyond the limit, but the computer can not calculate it.
Moreover, I believe that it can only be confirmed on supercomputer whether this is really counterexample.
In addition, it is necessary to make corrections in the supercomputer.

**Category:** Number Theory

[10] **viXra:1903.0296 [pdf]**
*submitted on 2019-03-15 19:04:45*

**Authors:** Masashi Furuta

**Comments:** 21 Pages.

We define the "Div sequence" that sets up the number of times divided by 2 in the Collatz operation.
Using this and the "infinite descent", we prove the Collatz conjecture.

**Category:** Number Theory

[9] **viXra:1903.0295 [pdf]**
*submitted on 2019-03-15 22:14:20*

**Authors:** Aaron Chau

**Comments:** 2 Pages.

也因为多与少，即填得满与填不满的视觉凭证是零点空格，所以，零点空格证明黎猜不成立。

**Category:** Number Theory

[8] **viXra:1903.0209 [pdf]**
*submitted on 2019-03-11 18:46:22*

**Authors:** Bambore Dawit Geinamo

**Comments:** 2 Pages. For more improvement comments and corrections are expected

This paper magically shows very interesting and simple proof of Fermata Last Theorem. The proof describes sufficient conditions of that the equation holds and contradictions on them to satisfy the theorem. If Fermat had proof most probably his proof may be similar with this one.

**Category:** Number Theory

[7] **viXra:1903.0200 [pdf]**
*replaced on 2019-03-13 09:22:44*

**Authors:** Maik Becker-Sievert

**Comments:** 1 Page.

Two cubes are a sum of nine cubes

**Category:** Number Theory

[6] **viXra:1903.0167 [pdf]**
*submitted on 2019-03-09 10:51:21*

**Authors:** Zeolla Gabriel Martín

**Comments:** 11 Pages. Idioma Español

Este documento desarrolla y demuestra el descubrimiento de un nuevo algoritmo de multiplicación que funciona absolutamente con todos los números.

**Category:** Number Theory

[5] **viXra:1903.0157 [pdf]**
*replaced on 2019-08-08 00:08:28*

**Authors:** Toshiro Takami

**Comments:** 56 Pages.

I also found a zero point which seems to deviate from 0.5.
I thought that the zero point outside 0.5 can not be found very easily in the area which can not be shown in the figure, but this area can not be represented in the figure but can be found one after another.
It is completely unknown whether this axis is distorted in the 0.5 axis or just by coincidence.
The number of zero points in the area that can not be shown in the figure is now 43.
No matter how you looked it was not found in other areas.
It seemed that there is no other way to interpret this axis as 0.5 axis is distorted in this area.
Somewhere on the net there is a memory that reads the mathematician's view that "there are countless zero points in the vicinity of 0.5 on high area".
We are reporting that the zero point search of the high-value area of the imaginary part which was giving up as it is no longer possible with the supercomputer is no longer possible, is reported.
43 zero-point searches in the high-value area of the imaginary part are thus successful.
This means that the zero point search in the high-value area of the imaginary part has succeeded in the 43.
We will also write 43 zero point searches of the successful high-value area of the imaginary part.
There are many counterexamples far beyond 0.5, which is far beyond the limit, but the computer can not calculate it.
Moreover, I believe that it can only be confirmed on supercomputer whether this is really counterexample. In addition, it is necessary to make corrections in the supercomputer.

**Category:** Number Theory

[4] **viXra:1903.0144 [pdf]**
*submitted on 2019-03-08 12:57:37*

**Authors:** Emmanuil Manousos

**Comments:** 10 Pages.

In this article, we define a pair of sequences (α, β). By using the properties of the pair (α, β), we establish a method for determining large prime numbers.

**Category:** Number Theory

[3] **viXra:1903.0059 [pdf]**
*replaced on 2019-11-05 14:26:42*

**Authors:** Espen Gaarder Haug, Pankaj Mani

**Comments:** 7 Pages.

In this paper, we point out an interesting asymmetry in the rules of fundamental mathematics between positive and negative numbers. Further, we show that there exists an alternative numerical system that is basically identical to today’s system, but where positive numbers dominate over negative numbers. This is like a mirror symmetry of the existing number system. The asymmetry in both of these systems leads to imaginary and complex numbers.
We also suggest an alternative number system with perfectly symmetrical rules – that is, where there is no dominance of negative numbers over positive numbers, or vice versa, and where imaginary and complex numbers are no longer needed. This number system seems to be superior to other numerical systems, as it brings simplicity and logic back to areas that have been dominated by complex rules for much of the history of mathematics. We also briefly discuss how the Riemann hypothesis may be linked to the asymmetry in the current number system.
The foundation rules of a number system can, in general, not be proven incorrect or correct inside the number system itself. However, the ultimate goal of a number system is, in our view, to be able to describe nature accurately. The optimal number system should therefore be developed with feedback from nature. If nature, at a very fundamental level, is ruled by symmetry, then a symmetric number system should make it easier to understand nature than a asymmetric number system would. We hypothesize that a symmetric number system may thus be better suited to describing nature. Such a number system should be able to get rid of imaginary numbers in space-time and quantum mechanics, for example, two areas of physics that to this day are clouded in mystery.

**Category:** Number Theory

[2] **viXra:1903.0031 [pdf]**
*submitted on 2019-03-02 16:28:58*

**Authors:** Ahmad Telfah

**Comments:** 10 pages

this paper carrying a method to introduce the distribution of the densities of the prime numbers and the composite numbers along in natural numbers, the method basically depends on the direct deduction of the composite numbers in a specified intervals that also with using some corrections and modifications to reach maximum and minimum values of the composites and primes densities, this allowed us to detect some special conjectures related to the primes density.

**Category:** Number Theory

[1] **viXra:1903.0030 [pdf]**
*submitted on 2019-03-02 16:40:03*

**Authors:** Ahmad Telfah

**Comments:** 5 pages

this paper carrying a method to calculate an approximation to the number of the prime numbers in the natural numbers interval I={1,2,3,4,……,P_n,P_n+1,P_n+2,……,P_n^2 } by using the primes (2,3,5,…,P_n ) to specify the primes density in the sub intervals I(P_n ) as
I(P_n )={P_n^2 〖,P〗_n^2+1,P_n^2+2,P_n^2+3,……,P_(n+1)^2-1} has primes density of (d(P_n ))= ( ∏_(i=1)^(i=n)▒〖( 1- 1/P_i 〗 ).

**Category:** Number Theory