# Sebastián Martín RuizI. E.S. Caepionis · Mathematics

Sebastián Martín Ruiz

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

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152

Citations

Introduction

I do research in number theory using the MATHEMATICA program

Additional affiliations

Education

September 2006 - June 2007

September 1984 - June 1991

September 1981 - June 1982

**Instituto Fernando Herrera**

Field of study

- Curso de Orientación Universitaria

## Publications

Publications (32)

In this article we give an elementary proof that the Riemann Hypothesis is false, based on Nicolas' Theorem.

In this article we give an elementary proof that the Riemann hypothesis is false, based onthe Nicolas' Theorem and my result by 1997.

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.

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.

In this article we extend the idea of prime factorization using trees.

In this article we gave a formula for the
n-th prime that involve only elementary operations
+ − × ÷ and the floor function.

The set of prime numbers is finite. An elementary proof.

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

Comments about the Euclid's proof of the infinitude of prime numbers. was Euclid wrong?

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

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.

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.

In this article we give a result obtained of an experimental way for the Euler totient function.

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.

In this article we gave a recurrence to obtain the n-th prime number as function of the (n-1)-th prime number.

In this article we see that the value takes the Smarandache Function when it is applied to a perfect number.

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.

Formula for the nth prime using elementary arithmetical functions based in a previous formula changing the characteristic function of prime numbers.

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.

In this article, a formula is given to obtain the next prime in an arithmetic progression.

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.

In this article we give a compilation of most of my formulas about prime numbers

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.

This article is the first recurrence that a did to obtain the prime numbers

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

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...

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)

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

A value or an approximation for zeta (3)?

Zeta(3)=387681796/9999999999*Pi^3

Zeta(3)=Sum1/n^3

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

This number is irrational?

Conjecture:

(q

^{2r}+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.)

These two series have the same sum.

What is the sum of this series?

Sum((n+1)

^{2}+n^{3})/(n^{3}(n+1)^{2})Sum((n+1)

^{3}+n^{2})/(n^{2}(n+1)^{3})from n = 1 to infinity

Sincerely

Sebastián Martín Ruiz

Prove the following result:

x=a

^{2}-b^{2}y=2ab

z=a

^{2}+b^{2}z

^{2}=x^{2}+y^{2}Then z

^{2 }- x·y/4 is composite and find the factorization.

Please check this last disproof of the Riemann hypothesis I just did. Can you find an error?

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.