# Number Theory

## 1911 Submissions

 viXra:1911.0525 [pdf] submitted on 2019-11-30 10:17:22

### II.La Conjetura de Collatz (continuación).

Authors: Miguel Cerdá Bennassar

Este escrito es continuación del publicado en Agosto 2019 con título "LA CONJETURA DE COLLATZ. Orden y armonía en los números de las secuencias".
Category: Number Theory

 viXra:1911.0484 [pdf] submitted on 2019-11-29 09:47:14

### Fermat Triples using Modular Arithmetic

Authors: James Edwin Rock

Andrew Wiles proved there are no integers x, y, and z and a prime p ≥ 3 with x^p+y^p +z^p=0. We use the Barlow relations to generate Fermat Triples where x^p+y^p +z^p ≡ 0 for an infinite number of moduli.
Category: Number Theory

 viXra:1911.0477 [pdf] submitted on 2019-11-28 02:22:12

### Evidence, that X^2+y^3=1 and Others Have no Solution in Q>0

Authors: Dmitri Martila

Due to the Incompleteness Theorems of Gödel one can say, that some true conjectures do not have valid proofs. One could think it also about my conjectures below, but I was lucky to find evidence for them.
Category: Number Theory

 viXra:1911.0426 [pdf] submitted on 2019-11-25 06:34:15

### A Nice Rational Estimator of the Fractional Part of the Square Root of Some Positive Integer

Authors: Juan Moreno Borrallo

In this paper it is proposed a nice rational estimator of the fractional part of the square root of any positive integer.
Category: Number Theory

 viXra:1911.0316 [pdf] submitted on 2019-11-18 11:12:58

### The Prime Counting Function and the Sum of Prime Numbers

Authors: Juan Moreno Borrallo

In this paper it is proved that the sum of consecutive prime numbers up to the square root of a given natural number is asymptotically equivalent to the prime counting function. Also, they are found some solutions such that both series are equal. Finally, they are listed the prime numbers at which both series are equal, and exposed some conjectures regarding this type of prime numbers.
Category: Number Theory

 viXra:1911.0310 [pdf] submitted on 2019-11-18 05:46:30

### 多 与 少 告 诉 我 们 黎 曼 伪 造 质 数

Authors: Aaron chau

Category: Number Theory

 viXra:1911.0308 [pdf] submitted on 2019-11-18 07:05:36

### The Goldbach Conjecture is True

Authors: James Edwin Rock

In the 17th century Christian Goldbach conjectured that any even number four or greater is the sum of two primes. This has never been proven, but it has been tested and shown to be true for all even numbers up to 4 x 10^18. We show the probability of this being false is about (1 / 10^98912 ) collectively for all even integers greater than 65,536,000 and drops to over ((1 / 10)^10)^14 collectively for all even integers greater than 4.5 x 10^18.
Category: Number Theory

 viXra:1911.0287 [pdf] submitted on 2019-11-17 08:18:55

### Recurring Pairs of Consecutive Entries in the Number-of-Divisors Function

Authors: Richard J. Mathar

The Number-of-Divisors Function tau(n) is the number of divisors of a positive integer n, including 1 and n itself. Searching for pairs of the format (tau(n), tau(n+1)), some pairs appear (very) often, some never and some --- like (1,2), (4,9), or (10,3) --- exactly once. The manuscript provides proofs for 46 pairs to appear exactly once and lists 12 pairs that conjecturally appear only once. It documents a snapshot of a community effort to verify sequence A161460 of the Online Encyclopedia of Integer Sequences that started ten years ago.
Category: Number Theory

 viXra:1911.0236 [pdf] submitted on 2019-11-13 14:02:48

### A Technical Report on 'The Inconsistency of Arithmetic' -- The Discussion

Authors: David Streit, Christoph Benzmüller, Ralf Wüsthofen

This document presents the discussion with two experts in automated theorem proving in the course of drawing up their technical report http://viXra.org/abs/1910.0115 on the paper 'The Inconsistency of Arithmetic' (http://vixra.org/abs/1904.0428). Main issue of the discussion is the wrong countermodel given in the report that is based on an incorrect application of predicate logic.
Category: Number Theory

 viXra:1911.0208 [pdf] submitted on 2019-11-11 14:09:39

### Refutation of the Aafrempong Conjecture

Authors: Colin James III

We evaluate the AAFrempong conjecture, named by the author after the name of the author, which states in any triangle, the sum of the lengths of any two sides is greater than the length of the third side, is not tautologous. This forms a non tautologous fragment of the universal logic VŁ4.
Category: Number Theory

 viXra:1911.0201 [pdf] replaced on 2019-11-15 16:55:20

### Prime Triplet Conjecture

Authors: Toshiro Takami

Prime Triplet and Twin Primes have exactly the same dynamics. All Prime Triplet are executed in hexagonal circulation. It does not change in a huge number (forever huge number). In the hexagon, Prime Triplet are generated only at (6n -1)(6n+1). [n is a positive integer] When the number grows to the limit, the denominator of the expression becomes very large, and primes occur very rarely, but since Prime Triplet are 35/12 times of the 3th power distribution of primes, the frequency of occurrence of Prime Triplet is very equal to 0. However, it is not 0. Therefore, Prime Triplet continue to be generated. If Prime Triplet is finite, the Primes is finite. The probability of Prime Triplet 35/12 times of the 3th power probability of appearance of the Prime. This is contradictory. Because there are an infinite of Primes. That is, Prime Triplet exist forever.
Category: Number Theory

 viXra:1911.0198 [pdf] submitted on 2019-11-11 07:34:34

### Analyzing Some Parts of Ramanujan’s Manuscripts: Mathematical Connections Between Several Ramanujan’s Equations, the Rogers-Ramanujan Continued Fractions and Some Sectors of Cosmology and Theoretical Physics. II

Authors: Michele Nardelli, Antonio Nardelli

In this research thesis, we have analyzed some parts of Ramanujan’s Manuscripts and obtained new mathematical connections between several Ramanujan’s equations, the Rogers-Ramanujan continued fractions and some sectors of Cosmology and Theoretical Physics
Category: Number Theory

 viXra:1911.0180 [pdf] replaced on 2019-11-15 06:50:44

### Prime Sextuplet Conjecture

Authors: Toshiro Takami

Prime Sextuplet and Twin Primes have exactly the same dynamics. All Prime Sextuplet are executed in hexagonal circulation. It does not change in a huge number (forever huge number). In the hexagon, Prime Sextuplet are generated only at (6n -1)(6n+5). [n is a positive integer] When the number grows to the limit, the denominator of the expression becomes very large, and primes occur very rarely, but since Prime Sextuplet are 48/3 times of the sixth power distribution of primes, the frequency of occurrence of Prime Quintuplet is very equal to 0. However, it is not 0. Therefore, Prime Sextuplet continue to be generated. If Prime Sextuplet is finite, the Primes is finite. The probability of Prime Sextuplet 48/3 times of the sixth power probability of appearance of the Prime. This is contradictory. Because there are an infinite of Primes. That is, Prime Sextuplet exist forever.
Category: Number Theory

 viXra:1911.0179 [pdf] replaced on 2019-11-15 18:54:39

### Prime Quintuplet Conjecture

Authors: Toshiro Takami

Prime Quintuplet and Twin Primes have exactly the same dynamics. All Prime Quintuplet are executed in hexagonal circulation. It does not change in a huge number (forever huge number). In the hexagon, Prime Quintuplet are generated only at (6n -1)(6n+5). [n is a positive integer] When the number grows to the limit, the denominator of the expression becomes very large, and primes occur very rarely, but since Prime Quintuplet are 96/3 times of the 5th power distribution of primes, the frequency of occurrence of Prime Quintuplet is very equal to 0. However, it is not 0. Therefore, Prime Quintuplet continue to be generated. If Prime Quintuplet is finite, the Primes is finite. The probability of Prime Quintuplet 96/3 times of the 5th power probability of appearance of the Prime. This is contradictory. Because there are an infinite of Primes. That is, Prime Quintuplet exist forever.
Category: Number Theory

 viXra:1911.0177 [pdf] replaced on 2019-11-15 17:13:24

### Sexy Primes Conjecture

Authors: Toshiro Takami

Sexy Primes Conjecture were prooved. Sexy Primes and Twin Primes and Cousin Primes have exactly the same dynamics. All Primes are executed in hexagonal circulation. It does not change in a huge number (forever huge number). In the hexagon, Sexy Primes are generated only at (6n+1)(6n -1). [n is a positive integer] When the number grows to the limit, the denominator of the expression becomes very large, and primes occur very rarely, but since Sexy Primes are 8/3 times the square of the distribution of primes, the frequency of occurrence of Sexy Primes is very equal to 0. However, it is not 0. Therefore, Sexy Primes continue to be generated. If Sexy Primes is finite, the Primes is finite. Because, Sexy Primes are 8/3 times the square of the distribution of primes. This is contradictory. Since there are an infinite of Primes. That is, Sexy Primes exist forever.
Category: Number Theory

 viXra:1911.0144 [pdf] replaced on 2019-11-15 16:58:49

Authors: Toshiro Takami

Prime Quadruplet and Twin Primes have exactly the same dynamics. All Prime Quadruplet are executed in hexagonal circulation. It does not change in a huge number (forever huge number). In the hexagon, Prime Quadruplet are generated only at (6n -1)(6n+5). [n is a positive integer] When the number grows to the limit, the denominator of the expression becomes very large, and primes occur very rarely, but since Prime Quadruplet are 16/3 of the fourth power distribution of primes, the frequency of occurrence of Prime Quadruplet is very equal to 0. However, it is not 0. Therefore, Cousin Primes continue to be generated. If Prime Quadruplet is finite, the Primes is finite. The probability of Prime Quadruplet 16/3 of the fourth power probability of appearance of the Prime. This is contradictory. Because there are an infinite of Primes. That is, Prime Quadruplet exist forever.
Category: Number Theory

 viXra:1911.0116 [pdf] submitted on 2019-11-06 12:19:15

### Analyzing Some Parts of Ramanujan’s Manuscripts. Mathematical Connections Between Several Ramanujan’s Equations, the Rogers-Ramanujan Continued Fractions and the Dilaton Value.

Authors: Michele Nardelli, Antonio Nardelli

In this research thesis, we have analyzed some parts of Ramanujan’s Manuscripts and obtained new mathematical connections between several Ramanujan’s equations, the Rogers-Ramanujan continued fractions and the Dilaton value.
Category: Number Theory

 viXra:1911.0111 [pdf] submitted on 2019-11-06 01:41:19

### The Nature of the Φ(m) Function

Authors: Wei Zhang

In number theory, for the continuous product formula Π(1-2/p), the meaning is unclear.This paper gives the definition and nature of Φ(m) function, as well as the relationship between Φ(m) and Euler’s totient function φ(m). In number theory, Euler function φ(m) is widely used, Φ(m) function if there are other applications, Some attempts are made in this paper.
Category: Number Theory

 viXra:1911.0095 [pdf] replaced on 2019-12-04 14:22:27

### Refutation of Incompletely Predictable Problems: Riemann Zeta and Eratosthenes Sieve

Authors: Colin James III

We evaluate the algorithm used for the sieve of Eratosthenes which is not tautologous, hence refuting the conjecture of incompletely predictable problems such as the Riemann zeta function. We also note that the mode of inference used throughout the source is induction. These results form a non tautologous fragment of the universal logic VŁ4.
Category: Number Theory

 viXra:1911.0093 [pdf] replaced on 2019-12-03 14:31:49

### Rigorous Proofs for Open Problems Riemann Hypothesis, Polignac's and Twin Prime Conjectures

Authors: John Yuk Ching Ting
Comments: 48 Pages. Rigorous proofs for Riemann hypothesis (and explaining the two types of Gram points) and Polignac's and Twin prime conjectures.

Mathematics for Incompletely Predictable Problems is associated with Incompletely Predictable problems containing Incompletely Predictable entities. Nontrivial zeros and two types of Gram points in Riemann zeta function (or its proxy Dirichlet eta function) together with prime and composite numbers from Sieve of Eratosthenes are Incompletely Predictable entities. Correct and complete mathematical arguments for first key step of converting this function into its continuous format version, and second key step of applying Information-Complexity conservation to this Sieve result in direct spin-offs from first step consisting of proving Riemann hypothesis (and explaining two types of Gram points), and second step consisting of proving Polignac's and Twin prime conjectures.
Category: Number Theory

 viXra:1911.0083 [pdf] replaced on 2019-11-15 17:22:58

### Cousin Primes Conjecture

Authors: Toshiro Takami

Cousin Primes Conjecture were performed using WolframAlpha and Wolfram cloud from the beginning this time, as in the case of the twin primes that we did the other day. Cousin Primes and Twin Primes have exactly the same dynamics. All Cousin Primes are executed in hexagonal circulation. It does not change in a huge number (forever huge number). In the hexagon, Cousin Primes are generated only at (6n+1)(6n+5). [n is a positive integer] When the number grows to the limit, the denominator of the expression becomes very large, and primes occur very rarely, but since Cousin Primes are 4/3 times the square of the distribution of primes, the frequency of occurrence of Cousin Primes is very equal to 0. However, it is not 0. Therefore, Cousin Primes continue to be generated. That is, Cousin Primes exist forever.
Category: Number Theory

 viXra:1911.0079 [pdf] submitted on 2019-11-05 09:08:26

### On Some New Mathematical Connections Between Ramanujan’s Sum of Two Cubes, ζ(2), π, ϕ, Ramanujan’s Mock Theta Functions and Various Sectors of Theoretical Physics

Authors: Michele Nardelli, Antonio Nardelli

In this research thesis, we have described some new possible mathematical connections between various equations concerning the Ramanujan’s sum of two cubes, ζ(2), π, ϕ, Ramanujan’s mock theta functions and some sectors of Theoretical Physics
Category: Number Theory

 viXra:1911.0061 [pdf] submitted on 2019-11-04 01:47:31

### Convergent SeriesⅢ

Authors: Yuji Masuda

This is a proof of some convergent series part3.
Category: Number Theory

 viXra:1911.0052 [pdf] replaced on 2019-11-03 01:39:24

### Convergent Series

Authors: Yuji Masuda

This is a proof of some convergent series.
Category: Number Theory

 viXra:1911.0049 [pdf] submitted on 2019-11-03 02:40:36

### Convergent SeriesⅡ

Authors: Yuji Masuda

This is a proof of some convergent series part2.
Category: Number Theory

 viXra:1911.0044 [pdf] submitted on 2019-11-03 07:05:12

### On the Fundamental Mathematical Constants π, ϕ, ζ(2), ζ(6), ζ(8) and ζ(10): New Interesting Mathematical Connections

Authors: Michele Nardelli, Antonio Nardelli

In this research thesis, we have described the new possible mathematical connections between the following fundamental mathematical constants: π, ϕ, ζ(2), ζ(6), ζ(8) and ζ(10)
Category: Number Theory

 viXra:1911.0020 [pdf] submitted on 2019-11-01 16:12:52

### Further Mathematical Connections Between the Dark Matter Candidate Particles, Some Ramanujan Formulas and the Physics of Black Holes. III

Authors: Michele Nardelli, Antonio Nardelli

In the present research thesis, we have obtained further interesting new possible mathematical connections concerning some sectors of Ramanujan’s mathematics, some sectors of Particle Physics, inherent principally the Dark Matter candidate particles and the physics of black holes (Ramanujan-Nardelli mock formula).
Category: Number Theory

 viXra:1911.0019 [pdf] submitted on 2019-11-01 17:30:43

### Riemann Hypothesis

Authors: Yuji Masuda