# A"Vertical"Generalization of the binary Goldbach's Conjecture as applied on primes with prime indexes of any order i (i-primes)

```@inproceedings{Druagoi2020AVerticalGeneralizationOT,
title={A"Vertical"Generalization of the binary Goldbach's Conjecture as applied on primes with prime indexes of any order i (i-primes)},
author={Andrei-Lucian Druagoi},
year={2020}
}```
This article is a very short version of our earlier paper (“The “Vertical” Generalization of the Binary Goldbach’s Conjecture as Applied on “Iterative” Primes with (Recursive) Prime Indexes (i-primeths)” [6]), a paper in which we have proposed a new generalization of the binary/“strong” Goldbach’s Conjecture (GC) briefly called “the Vertical Goldbach’s Conjecture” (VGC), which is essentially a metaconjecture, as VGC states an infinite number of Goldbach-like conjectures stronger than GC, which… Expand

#### References

SHOWING 1-10 OF 16 REFERENCES
The “Vertical” Generalization of the Binary Goldbach’s Conjecture as Applied on “Iterative” Primes with (Recursive) Prime Indexes (i-primeths)
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 newExpand
Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4⋅1018
• Computer Science, Mathematics
• Math. Comput.
• 2014
How the even Goldbach conjecture was confirmed to be true for all even numbers not larger than 4 · 1018 and how the counts of minimal Goldbach partitions and of prime gaps are in excellent accord with the predictions made using the prime k-tuple conjecture of Hardy and Littlewood are described. Expand
New Bounds and Computations on Prime-Indexed Primes
• Mathematics, Computer Science
• Integers
• 2013
This paper gives explicit upper and lower bounds for π2(x), the number of prime-indexed primes up to x, as well as upper andLower bounds on the n-th prime- indexed prime, all improvements on the bounds from 2009. Expand
A prime fractal and global quasi-self-similar structure in the distribution of prime-indexed primes
Let p(n) be the nth prime and p(p(n)) be the nth prime-indexed prime (PIP). The process of taking prime-indexed subsequences of primes can be iterated, and the number of such iterations is theExpand
On the fractal distribution of primes and prime-indexed primes by the binary image analysis
• Mathematics
• 2016
In this paper, the distribution of primes and prime-indexed primes (PIPs) is studied by mapping primes into a binary image which visualizes the distribution of primes. These images show that theExpand
Fractal in the statistics of Goldbach partition
• Mathematics, Physics
• 2006
Some interesting chaos phenomena have been found in the difference of prime numbers. Here we discuss a theme about the sum of two prime numbers, Goldbach conjecture. This conjecture states that anyExpand
HARALD CRAM ER AND THE DISTRIBUTION OF PRIME NUMBERS
er. We shall see how their legacy has inuenced research for most of the rest of the century, particularly through the 'schools' of Selberg, and of Erdos, and with the \large sieve" in the sixties.Expand
On the subsequence of primes having prime subscripts
• Mathematics
• 2009
We explore the subsequence of primes with prime subscripts, (qn), and derive its density and estimates for its counting function. We obtain bounds for the weighted gaps between elements of theExpand
Different Approaches to the Distribution of Primes
In this lecture celebrating the 150th anniversary of the seminal paper of Riemann, we discuss various approaches to interesting questions concerning the distribution of primes, including several thatExpand