Number Theory

1302 Submissions

[9] viXra:1302.0170 [pdf] submitted on 2013-02-28 08:55:04

Special Properties of the First Absolute Fermat Pseudoprime, the Number 561

Authors: Marius Coman
Comments: 6 Pages. A list with 23 interesting properties that I found regarding the number 561, in relation with other Carmichael numbers, other Fermat pseudoprimes to base 2, with primes or other integers.

Though is the first Carmichael number, the number 561 doesn’t have the same fame as the third absolute Fermat pseudoprime, the Hardy-Ramanujan number, 1729. I try here to repair this injustice showing few special properties of the number 561.
Category: Number Theory

[8] viXra:1302.0164 [pdf] submitted on 2013-02-25 14:35:28

Demonstration of the Goldbach Conjecture

Authors: Ibrahima Sambegou Diallo
Comments: 27 Pages. Here is the first part of this demonstration, which will soon be complemented. For mathematicians, the main challenge is to judge whether or not to use the Chebotarev theorem and asymptotic formulas for solving the Goldbach hypothesis. Happy reading!

The Goldbach conjecture is a matter of quantity of partitions of even numbers. This is a consequence of combined four tools: the Chebotarev's density theorem, the Inclusion– exclusion principle, the Prime number theorem and the Algorithms for evaluating π(x). By applying these tools on a family of arithmetic sequences, we can establish the validity of this conjecture.
Category: Number Theory

[7] viXra:1302.0144 [pdf] submitted on 2013-02-21 09:18:58

Formulas for Generating Primes Involving Emirps, Carmichael Numbers and Concatenation

Authors: Marius Coman
Comments: 5 Pages. An overview on the relation between emirps and concatenation, also with respect for the author's special numbers, Fermat pseudoprimes

Observations on generating primes or products of very few primes from reversible primes and Carmichael numbers using the method of concatenation.
Category: Number Theory

[6] viXra:1302.0130 [pdf] submitted on 2013-02-19 12:17:49

Essai Sur la Conjecture Des Nombres Premiers N² + 2

Authors: M. MADANI Bouabdallah
Comments: 04 Pages. French language

We try to prove the Conjecture on Prime Numbers (n² +1) by elementary geometry by using Pythagore,Fermat,Euler,Lagrange and Gauss theorems.
Category: Number Theory

[5] viXra:1302.0106 [pdf] replaced on 2013-04-06 09:54:57

New Finding of Number Theory

Authors: Liu Ran
Comments: 14 Pages.

Odd prime density regularity Odd composite number density regularity The limitation of odd number is composite number Natural number is limited Prime is limited
Category: Number Theory

[4] viXra:1302.0102 [pdf] submitted on 2013-02-16 01:42:53

An Corollary of Riemann Hypothesis

Authors: Jinhua Fei
Comments: 10 Pages.

This paper use Nevanlinna second fundamental theorem of the value distribution theory , give an corollary of Riemann hypothesis.
Category: Number Theory

[3] viXra:1302.0093 [pdf] submitted on 2013-02-14 12:46:52

On a New Type of Recurrent Sequences of Primes Acpow Chains

Authors: Marius Coman
Comments: 13 Pages. Definition and applications of ACPOW chains of primes.

An interesting type of recurrent sequences of primes which could eventually lead to longer chains of successive primes than known Cunningham chains or CPAP’s . Few conjectures including a stronger version of Legendre’s conjecture and one regarding the Fermat primes. A classification of the set of primes.
Category: Number Theory

[2] viXra:1302.0056 [pdf] submitted on 2013-02-09 16:17:07

On the Frequency of Twin Prime Pairs

Authors: Sidharth Ghoshal
Comments: 11 Pages.

The goal of the following document is to demonstrate a proof of the Twin Prime Conjecture by determining bounds for the number of twin prime pairs between a number and its square and then proving that the lower bound is always greater than 1 for sufficiently large numbers.
Category: Number Theory

[1] viXra:1302.0028 [pdf] submitted on 2013-02-05 09:16:20

A Formula for Generating Primes and a Possible Infinite Series of Poulet Numbers

Authors: Marius Coman
Comments: 3 Pages. A formula which might lead to a corespondence (maybe even a bijection) between the set of primes and a subset of Poulet numbers.

An amazingly easy to formulate but rich in consequences property of Fermat pseudoprimes to base 2 (Poulet numbers).
Category: Number Theory