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


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
(1) Francisco Welington de Sousa Lima, Professor, Dietrich Stauffer Laboratory for Computational Physics, Departamento de Física, Universidade Federal do Piaui, Teresina, Brazil.
(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


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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