The “Vertical” Generalization of the Binary Goldbach’s Conjecture as Applied on “Iterative” Primes with (Recursive) Prime Indexes (i-primeths)
Andrei-Lucian Drăgoi *
Independent Researcher in Mathematics, Physics and Biology, Street Aleea Arinii Dornei, nr. 11, bl. I9, Sc. A, ap. 4, et. 2, Bucuresti, Sector 6, Romania.
*Author to whom correspondence should be addressed.
Abstract
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.