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Sebastián Martín Ruiz

Sebastián Martín Ruiz
I. E.S. Caepionis · Mathematics

Licenciado en Matematicas por la Universidad de Sevilla. Diploma de Estudios Avanzados por la Universidad de Sevilla. Master en Matemáticas por la Universidad de Cádiz

About

32
Publications
17,277
Reads
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150
Citations
Citations since 2017
0 Research Items
73 Citations
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Introduction
Additional affiliations
September 2004 - July 2005
Universidad de Sevilla
Position
  • Diploma de Estudios Avanzados
Description
  • Diversos resultados sobre números primos y función de Smarandache.
January 1992 - June 2015
Junta De Andalucía
Position
  • Profesor de Enseñanza Secundaria
Description
  • He impartido clases de Matemáticas, Estadística, Ciencias Naturales, Ámbito Científico Tecnológico, Informática, Dibujo, Educación para la Ciudadanía. He sido tutor de grupo varios años y dos años jefe de departamento.
September 1991 - January 1992
Universidad de Sevilla
Position
  • Profesor Asociado
Description
  • Profesor sustituto impartiendo clases de matemática discreta.
Education
September 2006 - June 2007
Universidad de Cádiz
Field of study
  • Matemáticas
September 1984 - June 1991
Universidad de Sevilla
Field of study
  • Matemáticas
September 1981 - June 1982
Instituto Fernando Herrera
Field of study
  • Curso de Orientación Universitaria

Publications

Publications (32)
Article
Full-text available
In this article we give an elementary proof that the Riemann Hypothesis is false, based on Nicolas' Theorem.
Article
Full-text available
In this article we give an elementary proof that the Riemann hypothesis is false, based onthe Nicolas' Theorem and my result by 1997.
Article
Full-text available
In this article we give an elementary proof that the Riemann hypothesis is false, based on the Nicholas's Theorem and the Mertel's Theorem.
Article
Full-text available
Gleissberg cycle is a recurring climate period of 80 years duration. It is usually attributed to the influence of the Sun. In this article, we present a new hypothesis for the possible cause related to the magnetic field of Jupiter.
Research
Full-text available
In this article we extend the idea of prime factorization using trees.
Research
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In this article we gave a formula for the n-th prime that involve only elementary operations + − × ÷ and the floor function.
Research
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The set of prime numbers is finite. An elementary proof.
Book
Full-text available
p>A book for people who love numbers: Smarandache Function applied to perfect numbers, congruences. Also, the Smarandache Prime and Coprime functions in connection with the expressions of the prime numbers.</p
Research
Full-text available
Comments about the Euclid's proof of the infinitude of prime numbers. was Euclid wrong?
Article
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Comments about the Euclid's demonstration by reduction to the absurd of the infinitude of prime numbers. It is incorrect Euclid's proof? Sebastián Martín Ruiz
Article
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Using inequalities of Rosser and Schoenfeld, we complete the first author’s partial proof of exact formulas for the prime-counting function π(x) and the nth prime number pn. Only the four arithmetic operations and the floor function are involved in the formulas. We indicate how to modify them in order to accelerate their computation.
Article
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We present a limit formula for the harmonic number function. This formula shows clearly how this function cancels the exponential and asymptotically tends to identity function.
Article
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In this article we give a result obtained of an experimental way for the Euler totient function.
Article
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In this paper we present the definitions and some properties of several Samrandache Type Functions that are involved in many solved and unsolved problems and conjectures in number theory and recreational mathematics.
Article
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In this article we gave a recurrence to obtain the n-th prime number as function of the (n-1)-th prime number.
Article
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In this article we see that the value takes the Smarandache Function when it is applied to a perfect number.
Article
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In most text books on number theory Wilson Theorem is proved by applying Lagrange theorem concerning polynomial congruences.Hardy and Wright also give a proof using cuadratic residues. In this article Wilson theorem is derived as a corollary to an algebraic identity.
Article
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Formula for the nth prime using elementary arithmetical functions based in a previous formula changing the characteristic function of prime numbers.
Article
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In this article I give a generalization of the previous formulas [1],[2],[3] to obtain the following prime number, valid for any increasing sequence of positive integer numbers in the one that we know the algebraic expression of its nth term.
Article
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In this article, a formula is given to obtain the next prime in an arithmetic progression.
Article
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The sum of powers of positive divisors of an integer, expressed in terms of the floor function, provides the basis for another characterization of twin primes in particular, and of prime k-tuples generally. This elementary characterization is deployed in a software test for prime k-tuples using Mathematica.
Article
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In this article we give a compilation of most of my formulas about prime numbers
Article
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Using inequalities of Rosser and Schoenfeld, we prove formulas for pi(n) and the n-th prime that involve only the elementary operations +,-,/ on integers, together with the floor function. P. Sebah has pointed out that the formula for pi(n) operates in O(n^(3/2)) time.
Article
Full-text available
This article is the first recurrence that a did to obtain the prime numbers
Book
p>Un libro para los amantes de los números: La función de Smarandache aplicada a los números perfectos, congruencias. También, las funciones prima y coprima de Smarandache en conexión con expresiones de los números primos.</p
Article
Full-text available
I have fbund some new prime numbers using the PROTH program of Yves Gallot. Using this Program, I have found the following prime numbers: 3239·2 12345 +1with3720digitsa=3,a=77551·2 12345 +1with3721digitsa=5,a=77595·2 12345 +1with3721digitsa=5,a=119363·2 12321 +1with3713digitsa=5,a=7· Since the exponents of the first three numbers are Smarandache nu...
Article
Full-text available
El Paradoxismo es un movimiento de vanguardia en literatura, arte, filosofía, ciencia, basado en el excesivo uso de antítesis, antinomias, contradicciones, parábolas, rarezas, y paradojas en la creación artística.

Questions

Questions (24)
Question
I have found that with a new definition of prime number the number 1 is composite and its only proper divisor is the same.
We define sigma1*(n)=sigma1(n)-n-1.
and
n is composite if and only if sigma1*(n)=/=0
For example
sigma1*(6)=1+2+3+6-6-1=5=/=0
sigma1*(7)=1+7-7-1=0
In the case of the number 1 we have:
sigma1*(1)=1-(1+1)=-1=/=0
and therefore 1 is composite and -1 is a proper divisor in Z and then 1 is also a proper divisor of 1.
Can you comment this?
Sincerely
Sebastián Martín Ruiz
Question
A value or an approximation for zeta (3)?
Zeta(3)=387681796/9999999999*Pi^3
Zeta(3)=Sum1/n^3
Question
x>1 is prime if and only if
\tex \displaystyle{\sum_{i=1}^{\sqrt{x}} \left ( \left \lfloor \frac{x}{i} \right \rfloor- \left \lfloor \frac{x-1}{i}\right \rfloor \right )=1} \tex
Question
This number is irrational?
Conjecture:
(q2r+1)(1/r) is irrational for all q and r rational numbers q=/=0 and r=/=1.
(It is a generalization of a very important theorem that I will explain later.)
Question
These two series have the same sum.
What is the sum of this series?
Sum((n+1)2+n3)/(n3(n+1)2)
Sum((n+1)3+n2)/(n2(n+1)3)
from n = 1 to infinity
Sincerely
Sebastián Martín Ruiz
Question
Prove the following result:
x=a2-b2
y=2ab
z=a2+b2
z2=x2+y2
Then z- x·y/4 is composite
 and find the factorization.
Question
The Riemann Hypothesis is false. Is this last proof right?
In this article we give an elementary proof that the Riemann hypothesis is false, based on the Nicolas' Theorem and my result by 1997.

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