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Journal of Advances in Mathematics and Computer Science, ISSN: 2456-9968, ISSN: 2231-0851 (Past),Vol.: 25, Issue.: 2

Original-research-article

The “Vertical” Generalization of the Binary Goldbach’s Conjecture as Applied on “Iterative” Primes with (Recursive) Prime Indexes (i-primeths)

 

Andrei-Lucian Drăgoi1*

1Independent Researcher in Mathematics, Physics and Biology, Street Aleea Arinii Dornei, nr. 11, bl. I9, Sc. A, ap. 4, et. 2, Bucuresti, Sector 6, Romania.

Article Information
Editor(s):
(1) Francisco Welington de Sousa Lima, Professor, Dietrich Stauffer Laboratory for Computational Physics, Departamento de Física, Universidade Federal do Piaui, Teresina, Brazil.
Reviewers:
(1) Weijing Zhao, Civil Aviation University of China, China.
(2) A. N. Chavan, Shivaji University, India.
(3) Bilge Peker, Necmettin Erbakan University, Turkey.
Complete Peer review History: http://www.sciencedomain.org/review-history/21625

Abstracts

This article proposes a synthesized classification of some Goldbach-like conjectures, including those which are “stronger” than the Binary Goldbach’s Conjecture (BGC) and launches a new generalization of BGC briefly called “the Vertical Binary Goldbach’s Conjecture” (VBGC), which is essentially a meta-conjecture, as VBGC states an infinite number of conjectures stronger than BGC, which all apply on “iterative” primes with recursive prime indexes (i-primeths). VBGC was discovered by the author of this paper in 2007 and perfected (by computational verifications) until 2017 by using the arrays of matrices of Goldbach index-partitions, which are a useful tool in studying BGC by focusing on prime indexes. VBGC distinguishes as a very important conjecture of primes, with potential importance in the optimization of the BGC experimental verification (including other possible theoretical and practical applications in mathematics and physics) and a very special self-similar property of the primes set.

Keywords :

Primes with prime indexes; i-primeths; the Binary Goldbach Conjecture; Goldbach-like conjectures; the Vertical Binary Goldbach Conjecture.

Full Article - PDF    Page 1-32

DOI : 10.9734/JAMCS/2017/36895

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