Number Theory

1306 Submissions

[12] viXra:1306.0163 [pdf] submitted on 2013-06-19 08:26:25

Strong Relationship Between Prime Numbers and Sporadic Groups

Authors: Klaus Lange
Comments: 18 Pages.

This paper shows a strong relationship between sporadic groups and prime numbers. It starts with new properties for the well known supersingular prime numbers of the moonshine theory. These new properties are only a preparation for the main result of this paper to show that the sporadic groups are strongly connected to prime numbers.
Category: Number Theory

[11] viXra:1306.0161 [pdf] replaced on 2014-10-07 02:14:05

Proof of Fermat's Theorem

Authors: G. I. Ovchinnikov
Comments: 24 Pages.

In the article showed that the equation of Fermat’s theorem is a transcendental equation. This transcendental equation has no solution in integers. Therefore,Fermat's Last Theorem is true.
Category: Number Theory

[10] viXra:1306.0143 [pdf] submitted on 2013-06-18 03:59:05

The Best Theory of Arbitrarily Long Arithmetic Progressions of Primes

Authors: Chun-Xuan Jiang
Comments: 10 Pages. it is very important paper

Using Jiang function we find the best theory of arbitrarily long arithmetic progressions of primes
Category: Number Theory

[9] viXra:1306.0107 [pdf] replaced on 2014-07-19 23:26:08

Lucasian Primality Criteria for Specific Classes of Numbers of the Form K2^n-1

Authors: Predrag Terzic
Comments: Pages.

Polynomial time prime testing algorithms for specic classes of numbers of the form k2^n-1 are introduced .
Category: Number Theory

[8] viXra:1306.0086 [pdf] submitted on 2013-06-13 10:31:25

A Possible Unimportant But Sure Interesting Conjecture About Primes

Authors: Marius Coman
Comments: 2 Pages.

Studying, related to Fermat pseudoprimes, my main object of study, the concatenation and the primes of the form n*p – n + 1, where p is also prime, I found incidentally an interesting possible fact about primes. Because the proof or disproof of the conjecture, and also the consequences in the case that is true, are beyond me, I shall limit myself to enunciate the conjecture and give few examples.
Category: Number Theory

[7] viXra:1306.0059 [pdf] submitted on 2013-06-09 20:56:07

Cálculo de la Cantidad de Números Primos Que Hay Por Debajo de un Número Dado //// How to Calculate the Amount of Prime Numbers that Are Less Than a Given Number

Authors: Germán Paz
Comments: 92 Pages. En español. // In Spanish.

En este documento se explica un procedimiento para calcular la cantidad exacta de números primos que hay por debajo de cualquier número entero mayor que 4. Al momento de escribir este documento, se pensó que se había llegado a un resultado nuevo. Es por eso que este trabajo está escrito describiendo el mencionado procedimiento como algo nuevo. Sin embargo, mucho después de haber escrito este trabajo, se le señaló al autor que el procedimiento en cuestión ya había sido descubierto por Adrien-Marie Legendre.

De todos modos, este documento es útil para quien quiera entender el algoritmo de Legendre para calcular la cantidad exacta de números primos que hay por debajo de un número dado.

Para una demostración de las dos primeras fórmulas que aparecen en la pág. 72 (las cuales describen una de las propiedades del Triángulo de Pascal), ver (Lemas 3 y 6). Combinando lo explicado en la pág. 39 y en las págs. 60 a 72 con las mencionadas fórmulas de la pág. 72, se puede ver la relación que existe entre una de las propiedades del Triángulo de Pascal y el algoritmo de Legendre.

Éste es un trabajo muy antiguo. En algunos casos se usó una simbología distinta a la convencional.


In this paper we explain a procedure to calculate the exact amount of prime numbers that are less than an integer greater than 4. At the time of writing this paper, the author thought he had obtained a new result. This is why in this work the mentioned procedure is described as something new. However, a long time after this work had been written, it was pointed out to its author that the method described had already been discovered by Adrien-Marie Legendre.

Anyway, this paper is useful for anyone who wants to understand Legendre's algorithm to calculate the exact amount of primes that are less than a given number.

For a proof of the first two formulas that appear on page 72, see If we combine what is explained on page 39 and on pages 60 to 72 with the mentioned formulas on page 72, we will see that there exists a relation between one of the properties of Pascal's Triangle and Legendre's algorithm.

This is a very old work.

Category: Number Theory

[6] viXra:1306.0056 [pdf] submitted on 2013-06-08 16:54:19

Santilli-Jiang Isomathematics for Changing Modern Mathematics

Authors: Chun-Xuan Jiang
Comments: 5 Pages.

To generalise the modern mathematics we establish Santilli-Jiang isomathematics.
Category: Number Theory

[5] viXra:1306.0047 [pdf] submitted on 2013-06-07 12:49:48

Six Polynomials in One and Two Variables that Generate Poulet Numbers

Authors: Marius Coman
Comments: 3 Pages.

Fermat pseudoprimes were for me, and they still are, a class of numbers as fascinating as that of prime numbers; over time I discovered few polynomials that generate Poulet numbers (but not only Poulet numbers). I submitted all of them on OEIS; in this paper I get them together.
Category: Number Theory

[4] viXra:1306.0030 [pdf] submitted on 2013-06-06 10:26:04

Sequences of Pyramidal Numbers

Authors: Arun Muktibodh, Uzma Sheikh, Dolly Juneja, Rahul Barhate, Yogesh Miglani
Comments: 7 Pages.

Shyam Sunder Gupta [4] has de¯ned Smarandache consecutive and reversed Smarandache sequences of Triangular numbers. Del¯m F.M.Torres and Viorica Teca [1] have further investigated these sequences and de¯ned mirror and symmetric Smarandache sequences of Triangular numbers making use of Maple system. One of the authors A.S.Muktibodh [2] working on the same lines has de¯ned and investigated consecutive, reversed, mirror and symmetric Smarandache sequences of pentagonal numbers of dimension 2 using the Maple system. In this paper we have de¯ned and investigated the s-consecutive, s-reversed, s-mirror and s-symmetric sequences of Pyramidal numbers (Triangular numbers of dimension 3.) using Maple 6.
Category: Number Theory

[3] viXra:1306.0027 [pdf] submitted on 2013-06-06 04:56:34

A Possible Infinite Subset of Poulet Numbers Generated by a Formula Based on Wieferich Primes

Authors: Marius Coman
Comments: 2 Pages.

I was studying the Poulet numbers of the form n*p - n + 1, where p is prime, numbers which appear often related to Fermat pseudoprimes (see the sequence A217835 that I submitted to OEIS) when I discovered a possible infinite subset of Poulet numbers generated by a formula based on Wieferich primes (I pointed out 4 such Poulet numbers).
Category: Number Theory

[2] viXra:1306.0015 [pdf] submitted on 2013-06-04 13:56:05

File: Results on Square Numbers and How Can it Help for the Proof of the Goldbach Conjecture

Authors: Julien Laurendeau
Comments: 2 Pages.

I will explore Lagrange's four squares theorem,say how it could help proving the Goldbach conjecture and conjecture something.
Category: Number Theory

[1] viXra:1306.0006 [pdf] submitted on 2013-06-01 17:12:07

On the Singular Series in the Jiang Prime K-Tuple Theorem

Authors: Chun-Xuan Jiang
Comments: 6 Pages.

Using Jiang function we prove the Jiang prime k-tuple theorem.We find true singular series.
Category: Number Theory