Number Theory

1909 Submissions

[36] viXra:1909.0655 [pdf] replaced on 2019-10-22 16:43:33

Mathematics for Incompletely Predictable Problems: Spin-Offs from Converting Discrete Format Riemann Zeta Function Into Its Continuous Format Version

Authors: John Yuk Ching Ting
Comments: 21 Pages. Proof for Riemann hypothesis and explanations for manifested properties of two types of Gram points.

"Mathematics for Incompletely Predictable Problems" makes all mathematical arguments valid and complete in this current paper (based on first key step of converting Riemann zeta function into its continuous format version) and our next paper (based on second key step of applying Information-Complexity conservation to Sieve of Eratosthenes). Nontrivial zeros and two types of Gram points calculated using this function plus prime and composite numbers computed using this Sieve are defined as Incompletely Predictable entities. Euler product formula alternatively and perfectly represents Riemann zeta function but utilizes product over prime numbers instead of summation over natural numbers. Hence prime numbers are encoded in this function demonstrating deep connection between them. Direct spin-offs from first step consist of proving Riemann hypothesis and explaining manifested properties of both Gram points, and from second step consist of proving Polignac's and Twin prime conjectures. These mentioned open problems are defined as Incompletely Predictable problems.
Category: Number Theory

[35] viXra:1909.0654 [pdf] replaced on 2019-10-23 06:25:42

Mathematics for Incompletely Predictable Problems: Spin-Offs from Applying Information-Complexity Conservation to Sieve of Eratostheness

Authors: John Yuk Ching Ting
Comments: 21 Pages. Proofs for Polignac's and Twin prime conjectures.

"Mathematics for Incompletely Predictable Problems" makes all mathematical arguments valid and complete in our previous paper (based on first key step of converting Riemann zeta function into its continuous format version) and this current paper (based on second key step of applying Information-Complexity conservation to Sieve of Eratosthenes). Nontrivial zeros and two types of Gram points calculated using this function plus prime and composite numbers computed using this Sieve are defined as Incompletely Predictable entities. Euler product formula alternatively and perfectly represents Riemann zeta function but utilizes product over prime numbers instead of summation over natural numbers. Hence prime numbers are encoded in this function demonstrating deep connection between them. Direct spin-offs from first step consist of proving Riemann hypothesis and explaining manifested properties of both Gram points, and from second step consist of proving Polignac's and Twin prime conjectures. These mentioned open problems are defined as Incompletely Predictable problems.
Category: Number Theory

[34] viXra:1909.0653 [pdf] submitted on 2019-09-29 18:18:41

ζ(4), ζ(6).......ζ(80), ζ(82) Are Irrational Number

Authors: Toshiro Takami
Comments: 22 Pages.

ζ(4), ζ(6).......ζ(80), ζ(82) considered. From these equations, it can be said that ζ(4),ζ(6).......ζ(80),ζ(82) are irrational numbers. ζ(84),ζ(86) etc. can also be expressed by these equations. Because I use π2, these are to be irrational numbers. The fact that the even value of ζ(2n) is irrational can also be explained by the fact that each even value of ζ(2n) is multiplied by π2.
Category: Number Theory

[33] viXra:1909.0651 [pdf] submitted on 2019-09-29 20:49:56

Refutation of Disproof of One of Cantor's Cardinals

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 two integer lists to map real numbers as Cantor’s cardinals. The disproof of the conjecture that integer infinity is equivalent to real number infinity is not tautologous, so the disproof is refuted. However, this refutation does not automatically confirm the conjecture, forming a non tautologous fragment of the universal logic VŁ4.
Category: Number Theory

[32] viXra:1909.0649 [pdf] submitted on 2019-09-30 00:52:33

The Yeet Theorem

Authors: Yellocord soc.
Comments: 2 Pages.

Abstract. We provide a surprisingly elementary proof confirming the Yeet Conjecture [Kim14, Yel18], which states that 5^n = n5 for any positive integer n. Moreover, we resolve the ab-Yeet paradox, namely the observation that the quantum state of 5^ab can collapse to either of the values ab or 1. (It has been observed [Lee18] that 5^ab collapses to 1 with probability greater than e for some e > 0.)
Category: Number Theory

[31] viXra:1909.0618 [pdf] submitted on 2019-09-28 19:28:27

A Disproof to one of Cantor's Cardinals

Authors: Quoss P Wimblik
Comments: 1 Page.

By representing each Integer with 2 Integers we can account for all Real and transcendental numbers given Infinite Intgers.
Category: Number Theory

[30] viXra:1909.0534 [pdf] submitted on 2019-09-24 07:40:19

The Equation: Psi(q)=2

Authors: Edgar Valdebenito
Comments: 2 Pages.

In this note we give q=0.645..., such that : psi(q)=2, where psi(q) is the Ramanujan's theta function.
Category: Number Theory

[29] viXra:1909.0532 [pdf] submitted on 2019-09-24 07:43:29

On the Equation: Gamma(x)*gamma(x+1/2)=2

Authors: Edgar Valdebenito
Comments: 3 Pages.

We give the real roots of the equation: gamma(x)*gamma(x+1/2)=2 , x>0 ,where gamma(x) is the Gamma function.
Category: Number Theory

[28] viXra:1909.0530 [pdf] submitted on 2019-09-24 08:26:16

The Secret of Ishango – On the Helix Structure of Prime Numbers

Authors: Christof Born
Comments: 11 Pages.

The bones of Ishango were found in the 1950s by Belgian archaeologist Jean de Heinzelin near a Palaeolithic residence in Ishango, Africa. Inscriptions, which can be interpreted as numbers, make these bones the oldest mathematical find in human history. There are various scientific papers on the interpretation of the inscriptions. Interestingly, on one of the two bones, we also find the six consecutive prime numbers 5, 7, 11, 13, 17 and 19. Did Stone Age people already know the secret of the prime numbers? This question is explored in my mathematical essay “The Secret of Ishango”: an adventurous journey around the world – from Basel in Switzerland to Erode in India. The presumed connection between the numbers on the bones of Ishango and the structure of the prime numbers is illustrated by a sketch at the end of the text.
Category: Number Theory

[27] viXra:1909.0515 [pdf] submitted on 2019-09-24 21:25:35

The Requirements on the Non-trivial Roots of the Riemann Zeta via the Dirichlet Eta Sum

Authors: William Blickos
Comments: 11 Pages.

An explanation of the Riemann Hypothesis is given in 8 parts, with the first being a statement of the problem. In the next 3 parts, the complex valued Dirichlet Eta sum, a known equivalence to Riemann Zeta in the critical strip, is split into 8 real valued sums and 2 constants. Part 5 explains a recursive relationship between the 8 sums. Section 6 shows that the sums must individually equal 0. Part 7 details the ratios of the system when all sums equal 0 at once. Finally, part 8 solves the system in terms of the original Dirichlet Eta sum inputs. The result shows that the only possible solution for the real portion of the complex input, commonly labeled a, is that it must equal 1/2, and thus proves Riemann’s suspicion.
Category: Number Theory

[26] viXra:1909.0504 [pdf] submitted on 2019-09-25 04:22:09

Proof of Goldbach's Conjecture

Authors: Wu Ye TangYin
Comments: 12 Pages. NO

Prime number, compound number, prime factor decomposition, hypothesis. Theme: Integer theory. Push assumptions to infinity according to computational logic Random Extraction Computing Theory Welcome the distinguished gentleman (lady) to comment on my article
Category: Number Theory

[25] viXra:1909.0495 [pdf] submitted on 2019-09-23 16:00:16

Explicit Upper Bound for all Prime Gaps

Authors: Derek Tucker
Comments: 3 Pages.

Let p_s denote the greatest prime with squared value less than a given number. We call the interval from one prime’s square to the next, a prime’s season. By improving on the well known proof of arbitrarily large prime gaps, here we show that for all seasons, the upper bound of prime gap length is 〖2p〗_s.
Category: Number Theory

[24] viXra:1909.0473 [pdf] replaced on 2019-09-24 21:05:39

Formula of ζ Even-Numbers

Authors: Toshiro Takami
Comments: 16 Pages.

I published the odd value formula for ζ, but I realized that this was true even when it was even. Therefore, it will be announced.
Category: Number Theory

[23] viXra:1909.0461 [pdf] replaced on 2019-10-01 10:30:58

Fibonacci's Answer to Primality Testing?

Authors: Julian TP Beauchamp
Comments: 8 Pages.

In this paper, we consider various approaches to primality testing and then ask whether an effective deterministic test for prime numbers can be found in the Fibonacci numbers.
Category: Number Theory

[22] viXra:1909.0456 [pdf] submitted on 2019-09-22 02:26:58

On the Ramanujan’s Fundamental Formula for Obtain a Highly Precise Golden Ratio: Mathematical Connections with Black Holes Entropies and Like-Particle Solutions

Authors: Michele Nardelli, Antonio Nardelli
Comments: 79 Pages.

In the present research thesis, we have obtained various and interesting new mathematical connections concerning the fundamental Ramanujan’s formula to obtain a highly precise golden ratio, some sectors of Particle Physics and Black Holes entropies.
Category: Number Theory

[21] viXra:1909.0385 [pdf] replaced on 2019-09-29 23:13:57

Formula of ζ Odd-Numbers

Authors: Toshiro Takami
Comments: 33 Pages.

I tried to find a new expression for zeta odd-numbers. It may be a new expression and will be published here. The correctness of this formula was confirmed by WolframAlpha to be numerically com- pletely correct.
Category: Number Theory

[20] viXra:1909.0384 [pdf] replaced on 2019-09-23 03:33:35

ζ(4), ζ(6).......ζ(108), ζ(110) Are Irrational Number

Authors: Toshiro Takami
Comments: 9 Pages.

ζ(4), ζ(6).......ζ(108), ζ(110) considered. From these equations, it can be said that ζ(4),ζ(6).......ζ(108),ζ(110) are irrational numbers. ζ(112),ζ(114) etc. can also be expressed by these equations. Because I use π2, these are to be irrational numbers. The fact that the even value of ζ(2n) is irrational can also be explained by the fact that each even value of ζ(2n) is multiplied by π2.
Category: Number Theory

[19] viXra:1909.0378 [pdf] submitted on 2019-09-19 04:18:29

La Conjetura DE Collatz. Orden Y Armonía en Los Números de Las Secuencias.

Authors: Miguel Cerdá Bennassar
Comments: 34 Pages.

Propongo una tabla numérica en la que se demuestra visualmente que las secuencias formadas con el algoritmo de Collatz acaban siempre en el número 1.
Category: Number Theory

[18] viXra:1909.0370 [pdf] submitted on 2019-09-17 13:19:02

On the Integer Solutions to the Equation X!+x=x^n

Authors: Miika Rankaviita
Comments: 20 Pages. Licencing: CC BY-SA

This thesis explains the solution to the problem of finding all of the integer pair solutions to the equation x!+x=x^n. A detailed explanation is given so that anyone with high school mathematics background can follow the solution. This paper is a translation of my diplom work in Vaasa Lyseo Upper Secondary School.
Category: Number Theory

[17] viXra:1909.0337 [pdf] submitted on 2019-09-17 00:13:09

A Definiive Proof of the ABC Conjecture

Authors: Abdelmajid Ben Hadj Salem
Comments: 10 Pages. We give another proof of the conjecture c

In this paper, we consider the $abc$ conjecture. Firstly, we give anelementaryproof the conjecture $c<rad^2(abc)$. Secondly, the proof of the $abc$ conjecture is given for $\epsilon \geq 1$, then for $\epsilon \in ]0,1[$. We choose the constant $K(\epsilon)$ as $K(\epsilon)=e^{\left(\frac{1}{\epsilon^2} \right)}$. Some numerical examples are presented.
Category: Number Theory

[16] viXra:1909.0334 [pdf] submitted on 2019-09-17 02:04:19

The Characteristic of Primes

Authors: Ihsan Raja Muda Nasution
Comments: 2 Pages.

In this paper, we propose the axiomatic regularity of prime numbers.
Category: Number Theory

[15] viXra:1909.0315 [pdf] replaced on 2019-09-27 19:16:23

ζ(5), ζ(7)..........ζ(331), ζ(333) Are Irrational Number

Authors: Toshiro Takami
Comments: 34 Pages.

Using the fact that ζ(3) is an irrational number, I prove that ζ(5), ζ(7)...........ζ(331) and ζ(333) are irrational numbers. ζ(5), ζ(7)...........ζ(331) and ζ(333) are confirmed that they were in perfect numerical agreement. This is because I created an odd-number formula for ζ, and the formula was created by dividing the odd- number for ζ itself into odd and even numbers.
Category: Number Theory

[14] viXra:1909.0312 [pdf] submitted on 2019-09-14 06:51:50

A Generalization of the Functional Equation of the Riemann zeta Function

Authors: Antoine Balan
Comments: 2 pages, written in french

With help of theta functions, a generalization of the functional equation of the zeta Riemann function can be defined.
Category: Number Theory

[13] viXra:1909.0305 [pdf] submitted on 2019-09-14 13:53:36

On the Ramanujan Modular Equations, Class Invariants and Mock Theta Functions: New Mathematical Connections with Some Particle-Like Solutions, Black Holes Entropies, ζ(2) and Golden Ratio

Authors: Michele Nardelli, Antonio Nardelli
Comments: 196 Pages.

In the present research thesis, we have obtained various interesting new possible mathematical connections between the Ramanujan Modular Equations, Class Invariants, the Mock Theta Functions, some particle-like solutions, Black Holes entropies, ζ(2) and Golden Ratio
Category: Number Theory

[12] viXra:1909.0299 [pdf] submitted on 2019-09-15 01:39:20

Collatz Conjecture Explained Through Recursive Functions

Authors: Natalino Sapere
Comments: 9 Pages. None

This paper explains the Collatz Conjecture through the use of recursive functions.
Category: Number Theory

[11] viXra:1909.0295 [pdf] submitted on 2019-09-15 05:25:01

On Prime NumberⅣ

Authors: Yuji Masuda
Comments: 1 Page.

This is primes④
Category: Number Theory

[10] viXra:1909.0285 [pdf] submitted on 2019-09-13 19:27:39

Polygonal Numbers in Terms of the Beta Function

Authors: Alfredo Olmos, R. Romyna Olmos
Comments: 7 Pages.

In this article we study some characteristics of polygonal numbers, which are the positive integers that can be ordered, to form a regular polygon. The article is closed, showing the relation of the polygonal numbers, with the Beta function when expressing any polygonal number, as a sum of terms of the Beta function.
Category: Number Theory

[9] viXra:1909.0178 [pdf] submitted on 2019-09-08 12:33:13

Riemann Hypothesis Proof by Hadamard Product and Monotonicity

Authors: Shekhar Suman
Comments: 5 Pages.

Analytic continuation by hadamard product is strictly monotonic which implies RH
Category: Number Theory

[8] viXra:1909.0165 [pdf] replaced on 2019-11-02 02:24:43

A Proof of Goldbach's Binary Conjecture

Authors: Sitangsu Maitra
Comments: 6 pages

Proof of Goldbach's strong conjecture in a different way
Category: Number Theory

[7] viXra:1909.0154 [pdf] submitted on 2019-09-07 13:41:13

On Prime NumbersⅢ

Authors: Yuji Masuda
Comments: 1 Page.

This is on primes3.
Category: Number Theory

[6] viXra:1909.0103 [pdf] submitted on 2019-09-05 18:48:43

On Prime Numbers Ⅱ

Authors: Yuji Masuda
Comments: 1 Page.

This is on primes.
Category: Number Theory

[5] viXra:1909.0059 [pdf] submitted on 2019-09-03 23:11:41

If Riemann’s Zeta Function is True, it Contradicts Zeta’s Dirichlet Series, Causing "Explosion". If it is False, it Causes Unsoundness.

Authors: Ayal Sharon
Comments: 32 Pages. Approx. 7500 words, and approx. 130 references in the bibliography

Riemann's "analytic continuation" produces a second definition of the Zeta function, that Riemann claimed is convergent throughout half-plane $s \in \mathbb{C}$, $\text{Re}(s)\le1$, (except at $s=1$). This contradicts the original definition of the Zeta function (the Dirichlet series), which is proven divergent there. Moreover, a function cannot be both convergent and divergent at any domain value. In other mathematics conjectures and assumed-proven theorems, and in physics, the Riemann Zeta function (or the class of $L$-functions that generalizes it) is assumed to be true. Here the author shows that the two contradictory definitions of Zeta violate Aristotle's Laws of Identity, Non-Contradiction, and Excluded Middle. The of Non-Contradiction is an axiom of classical and intuitionistic logics, and an inherent axiom of Zermelo-Fraenkel set theory (which was designed to avoid paradoxes). If Riemann's definition of Zeta is true, then the Zeta function is a contradiction that causes deductive "explosion", and the foundation logic of mathematics must be replaced with one that is paradox-tolerant. If Riemann's Zeta is false, it renders unsound all theorems and conjectures that falsely assume that it is true. Riemann's Zeta function appears to be false, because its derivation uses the Hankel contour, which violates the preconditions of Cauchy's integral theorem.
Category: Number Theory

[4] viXra:1909.0038 [pdf] submitted on 2019-09-02 12:25:38

Zeroes of The Riemann Zeta Function and Riemann Hypothesis

Authors: Shekhar Suman
Comments: 5 Pages.

Modulus of Hadamard product is shown increasing which proves the Riemann Hypothesis
Category: Number Theory

[3] viXra:1909.0027 [pdf] submitted on 2019-09-01 12:06:47

Mirror Sieves :Goldbach vs Matiyasevich

Authors: Francis Maleval
Comments: 1 Page.

The sieve of the addition of two prime numbers and the sieve of the product of two natural numbers are linked by a paradox of symmetrical objects. Goldbach's conjecture, additive version of a property of primes, would then have no chance being demonstrated if its multiplicative alter ego remained impenetrable to the disorder of prime numbers.
Category: Number Theory

[2] viXra:1909.0019 [pdf] submitted on 2019-09-01 21:24:11

Prime Number Pattern 7

Authors: Zeolla Gabriel Martín
Comments: 4 Pages.

This document exposes the construction of infinite patterns for prime numbers smaller than P. In this case, the pattern for prime numbers less than 11 is graphic.
Category: Number Theory

[1] viXra:1909.0010 [pdf] submitted on 2019-09-01 01:13:44

New Patterns of Modular Arithmetics

Authors: Kurmet Sultan
Comments: 1 Page. This Russian version of the article.

The article reports on the new patterns of modular arithmetic.
Category: Number Theory