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January 1992 - June 2015
- Profesor de Enseñanza Secundaria
- 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.
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.
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 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 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.
In this article I give a generalization of the previous formulas ,, 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.
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.
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.
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.
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.
n is composite if and only if sigma1*(n)=/=0
In the case of the number 1 we have:
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?
Sebastián Martín Ruiz
This number is irrational?
(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.)
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.