# Number Theory

## 1802 Submissions

 viXra:1802.0433 [pdf] submitted on 2018-02-28 20:58:26

### On the Computation of Primes & Semi-Primes

Authors: Clive Jones

Featuring the PF5 Function
Category: Number Theory

 viXra:1802.0427 [pdf] submitted on 2018-02-28 07:01:31

### The Dottie Number

Authors: Edgar Valdebenito

This note presents some formulas related with Dottie number.
Category: Number Theory

 viXra:1802.0395 [pdf] submitted on 2018-02-26 20:37:20

### Goldbach's Numbers

Abstract: Goldbach's conjectures are inseparable and both of them stem from an underlying fundamental structure of the natural numbers.Thus, one of them must consistently imply the other one, and the Goldbach's weak conjecture must imply the Goldbach's strong conjecture. Finally, all natural numbers are the Goldbach's numbers.
Category: Number Theory

 viXra:1802.0363 [pdf] submitted on 2018-02-26 10:46:52

### 13-Golden Pattern

Authors: Zeolla Gabriel martin

This paper develops the divisibility of the so-called Simple Primes numbers-13, the discovery of a pattern to infinity, the demonstration of the inharmonics that are 2,3,5,7,11,13 and the harmony of 1. The discovery of infinite harmony represented in fractal numbers and patterns. This is a family before the prime numbers. This paper develops a formula to get simple prime number-13 and simple composite number-13 The simple prime numbers-13 are known as the 17-rough numbers.
Category: Number Theory

 viXra:1802.0353 [pdf] replaced on 2018-03-08 04:44:34

### Prime Function Complete Proof

Authors: Dave Ryan T. Cariño

Function and method for solving the distribution of prime numbers accurately using the combination of step functions, polynomial functions, inverse functions and continuous functions. Equation 〖lim┬(n→∞) p(n)〗⁡〖={3+2(n+x_p )├|x_p=x_3+x_5+x_7+x_11+⋯x_p ┤}〗 is true for all integer where n>0 for the distribution and generation of exact values of prime numbers without exception. This formula is efficient by means of modern supercomputers for the task of expanding term x_p.
Category: Number Theory

 viXra:1802.0321 [pdf] submitted on 2018-02-22 07:29:28

### A Combinatorial Approach to the Last Theorem of Fermat

Authors: Andrea Prunotto

The condition of equiprobability among two events involving independent extractions of elements from a finite set is shown to coincide with Fermat's Diophantine equation. The problem of the division of the stakes, related to the events, is also discussed
Category: Number Theory

 viXra:1802.0303 [pdf] submitted on 2018-02-22 00:31:26

### Analysis of the Matrix Xjk=[x(j,k)] ∈C Where X(j,k)=δ+ω(α+βj)^φk

Authors: Pedro Caceres

The function x(j,k)=δ+ω(α+βj)^φk in C→C is a generalization of the power function y(α)=α^k in R→R and the exponential function y(k)=α^k in R→R. In this paper we are going to calculate the values of infinite and partial sums and products involving elements of the matrix Xjk=[x(j,k)]∈C As a result, several new representations will be made for some infinite series, including the Riemann Zeta Function in C.
Category: Number Theory

 viXra:1802.0269 [pdf] submitted on 2018-02-19 17:14:55

### Riemann's Analytic Continuation of Zeta(s) Contradicts the Law of the Excluded Middle, and is Derived by Using Cauchy's Integral Theorem While Contradicting the Theorem's Prerequisites

Authors: Ayal Sharon

The Law of the Excluded Middle holds that either a statement "X" or its opposite "not X" is true. In Boolean algebra form, Y = X XOR (not X). Riemann's analytic continuation of Zeta(s) contradicts the Law of the Excluded Middle, because the Dirichlet series Zeta(s) is proven divergent in the half-plane Re(s)<=1. Further inspection of the derivation of Riemann's analytic continuation of $\zeta(s)$ shows that it is wrongly based on the Cauchy integral theorem, and thus false.
Category: Number Theory

 viXra:1802.0236 [pdf] submitted on 2018-02-18 17:27:55

### 11-Golden Pattern

Authors: Zeolla Gabriel martin

This paper develops the divisibility of the so-called Simple Primes numbers-11 (1 to 11), the discovery of a pattern to infinity, the demonstration of the Inharmonics that are 2,3,5,7 and 11 and the harmony of 1. The discovery of infinite harmony represented in fractal numbers and patterns. This is a family before the prime numbers. The simple prime numbers-11 are known as the 13-rough numbers.
Category: Number Theory

 viXra:1802.0213 [pdf] submitted on 2018-02-17 10:38:14

### Existence Of Prime Numbers In Subsets Of The Oppermann's Intervals

Authors: ANIRILASY Méleste

We suggest that there exists, at least, one prime number in four intervals between n² and (n+1)² for any integer n 2 such that : all intervals are half-open; the excluded endpoints are multiples of n; the number of elements in each interval is equal to the least even upper bound for the biggest prime number strictly less than n. This conjecture is a strong form of Oppermann’s one.
Category: Number Theory

 viXra:1802.0201 [pdf] submitted on 2018-02-15 12:14:36

### 5-Golden Pattern

Authors: Zeolla Gabriel martin

This paper develops the divisibility of the so-called Simple Primes numbers-5, the discovery of a pattern to infinity, the demonstration of the inharmonics that are 2,3,5 and the harmony of 1. The discovery of infinite harmony represented in fractal numbers and patterns. This is a family before the prime numbers. This paper develops a formula to get simple prime number-5 and simple composite number-5 The simple prime numbers-5 are known as the 7-rough numbers.
Category: Number Theory

 viXra:1802.0198 [pdf] replaced on 2018-09-18 15:46:04

### Solving Riemann Hypothesis, Polignac's and Twin Prime Conjectures as Incompletely Predictable Problems

Authors: John Yuk Ching Ting
Comments: 45 Pages. This research paper contains proposed proofs for Riemann hypothesis, Polignac's and Twin prime conjectures

Riemann hypothesis refers to the proposal on Riemann zeta function whereby all of its nontrivial zeros are (mathematically) conjectured to lie on the critical line or [equivalently stated in this research paper] all of its nontrivial zeros are (geometrically) conjectured to exactly match the 'Origin' intercepts. This proposal will also culminate in allowing us to secondarily explain the closely related Gram points of this function. Involving proposals on infinity magnitude of both prime gaps and their associated sets of prime numbers, Twin prime conjecture deals with prime gap = 2 (representing twin primes) and is thus a subset of Polignac's conjecture which deals with all even number prime gaps = 2, 4, 6,... (representing prime numbers in totality except for the first prime number '2'). Both nontrivial zeros and prime numbers are Incompletely Predictable entities allowing us to employ our Virtual Container Research Method to solve the associated hypothesis and conjectures.
Category: Number Theory

 viXra:1802.0176 [pdf] submitted on 2018-02-14 10:10:56

### Diophantine Quintuples over Quadratic Rings

Authors: Philip Gibbs

A Diophantine m-tuple is a set of m distinct non-zero integers such that the product of any two elements of the set is one less than a square. The definition can be generalised to any commutative ring. A computational search is undertaken to find Diophantine 5-tuples (quintuples) over the ring of quadratic integers Z[√D] for small positive and negative D. Examples are found for all positive square-free D up to 22, but none are found for the complex rings including the Gaussian integers.
Category: Number Theory

 viXra:1802.0154 [pdf] replaced on 2018-02-14 09:08:19

### Generalized Conjecture on the Distribution of Prime Numbers

Authors: Réjean Labrie

Abstract: Let N, n and k be integers larger than 1. Then for all N there exists a minimum threshold k such that for n>=N, if we cut the sequence of consecutive integers from 1 to n*(n+k) into n+k slices of length n, we always find at least a prime number in each slice. It follows that π(n*(n+k)) > π(n*(n+k-1)) > π(n*(n+k-2)) > π(n*(n+k-3))> ...> π(2n)> π(n) where π(n) is the quantity of prime numbers smaller than or equal to n.
Category: Number Theory

 viXra:1802.0141 [pdf] submitted on 2018-02-12 14:37:55

### Observations on Poulet Numbers Having Only Odd Digits Based on Their Reversals

Authors: Marius Coman

The set of Poulet numbers having only odd digits is: 1333333, 1993537, 3911197, 5351537, 5977153, 7759937, 11777599...(22 from the first 7196 Poulet numbers belong to this set). Question: is this sequence infinite? Observations: the numbers n*P + R(P) – n respectively P + n*R(P) - n, where R(P) is the reversal of P and n positive integer, are often primes. Examples: for P = 1333333, the number 1333333 + 3333331 – 1 = 4666663, prime; also 3*1333333 + 3333331 – 3 = 7333327, prime; also 5*1333333 + 3333331 – 5 = 9999991, prime. For the same P, the number 1333333 + 2*3333331 - 2 = 7999993, prime; also the number 1333333 + 4*3333331 - 4 = 14666653, prime.
Category: Number Theory

 viXra:1802.0135 [pdf] submitted on 2018-02-13 02:20:28

### Primes of the Form N∙P+R(P)-N Where P Primes Having Only Odd Digits and R(P) Their Reversals

Authors: Marius Coman

In a previous paper I noticed that the numbers n*P + R(P) – n respectively P + n*R(P) - n, where P are Poulet numbers having only odd digits, R(P) the reversals of P and n positive integer, are often primes. In this paper I notice that the same is true for primes having only odd digits (see A030096 in OEIS for a list of such primes). Taken thirteen randomly chosen consecutive primes P having nine (odd) digits (from 971111137 to 971111993) I see that for all of them there exist at least a value of n smaller than 15 for which the number n*P + R(P) – n is prime (for 971111591, for instance, there exist four such values of n: 9, 11, 14, 15; for 971111137 three: 2, 4, 7; for 971111551 also three: 1, 2, 6; for 971111959 also three: 1, 9, 10; for 971111993 also three: 5, 6, 14).
Category: Number Theory

 viXra:1802.0134 [pdf] submitted on 2018-02-11 06:47:29

### Bexar County Detention Paper Number Theory Topological Equation

Authors: Ricardo Gil
Comments: 1 Page. There are alot of collected papers at Bexar County which I submitted to the Government.

Bexar County Detention Papers (Topological Number Theory Formula/Equation/Algorithm) By Ricard.gil@sbcglobal.net January 9,2017 to Pretrail (Court February 26,2018 CCC4) The objective of this paper is to show how one can take Gigori Pereleman complex arXiv 39 page paper and make it into a simple topological formula. I am revealing the ide I had in Bexar County Detention on viXra. I want to dedicate the Bexar County Detention papers to my Ex-Wife, Eddie Gil and Ashleigh Gil. (See attached Photo) & I can always be found at 3607 Ticonderoga, San Antonio Texas, where I am a permanent guest/resident. I. The Topological Formula/Equation/Algorithm 1D=2D=3D/1=1/1D=2D=3D
Category: Number Theory

 viXra:1802.0097 [pdf] submitted on 2018-02-08 06:40:23

### Boundedness of a Function of Fibonacci Numbers in Generic Form and Its Limit at Infinity.

Authors: Jesús Álvarez Lobo
Comments: 3 Pages. Revista Escolar de la Olimpiada Iberoamericana de Matemática. Volume 34.

In this paper is proved an inequality involving a function of Fibonacci numbers in generic form and its limit at infinity is calculated using the asymptotic relationship given by Barr and Schooling in "The Field" (December 14, 1912).
Category: Number Theory

 viXra:1802.0095 [pdf] submitted on 2018-02-08 06:59:49

### PMO33.2. Problema del Duelo Matemático 08 (Olomouc, Chorzow, Graz).

Authors: Jesús Álvarez Lobo
Comments: 2 Pages. Spanish.

Solution to the problem PMO33.2. Problem of Mathematical Duel 08 (Olomouc, Chorzow, Graz). Determine all triples (x, y, z) of positive integers verifying the following equation: 3 + x + y + z = xyz
Category: Number Theory

 viXra:1802.0093 [pdf] submitted on 2018-02-08 07:18:35

### Lobo's Theorem for Heronian Triangles (Problem Proposed by K.R.S. Sastry, Bangalore, India)

Authors: Jesús Álvarez Lobo
Comments: 1 Page. Revista Escolar de la Olimpiada Iberoamericana de Matemática. Volume 21. Spanish.

Lobo's theorem for heronian triangles: "Exists at least one heronian triangle such that two sides are consecutive natural numbers and its area is equal to n times the perimeter, for n = 1, 2, 3". Teorema de Lobo para triángulos heronianos: Existe al menos un triángulo heroniano tal que dos de sus lados son números naturales consecutivos y su área es igual a n veces su perímetro, para n = 1, 2, 3.
Category: Number Theory

 viXra:1802.0039 [pdf] submitted on 2018-02-05 04:50:15

### A Diophantine Equation as a Condition of Equiprobability

Authors: Andrea Prunotto