二元哥德巴赫猜想在素数指数为任意阶i的素数（i-素数）上的“垂直”推广
A "Vertical" Generalization of the binary Goldbach's Conjecture as applied on primes with prime indexes of any order i (i-primes)
摘要：
这篇文章是基于我们早期的论文的调查（“应用于具有（递归）素数指数的”迭代“素数的二进制哥德巴赫猜想的”垂直“推广”）（i-primeths）”[11]），其中我们提出了一个新的推广的二进制/“强”哥德巴赫猜想（GC）简称为“垂直哥德巴赫猜想”（VGC），这本质上是一个元猜想，因为VGC陈述了一个比GC更强的有限数量的类似哥德巴赫的结构，这些结构都适用于具有递归素数索引的“迭代”素数（称为“i-素数”）。VGC是由本文作者在2007年发现的，之后它被改进和扩展（通过计算验证）直到现在（2020年）。VGC区分为一个非常重要的素数“元猜想”，因为它陈述了一个新的类，包含比GC更强/更严格的无限数量的命题。VGC在优化GC实验验证（包括其他可能的数学和物理理论和实际应用）方面具有巨大的潜在重要性。VGC也可以看作是素数分布的一种非常特殊的自相似性质。本综述包含了一些关于VGC的新结果。
英文摘要：
This article is a survey based on our earlier paper ("The 'Vertical' Generalization of the Binary Goldbach's Conjecture as Applied on 'Iterative' Primes with (Recursive) Prime Indexes (i-primeths)" [11]), 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 meta-conjecture, as VGC states an in finite number of Goldbach-like conjectures stronger than GC, which all apply on "iterative" primes with recursive prime indexes (named "i-primes"). VGC was discovered by the author of this paper in 2007, after which it was improved and extended (by computational verifications) until the present (2020). VGC distinguishes as a very important "meta-conjecture" of primes because it states a new class containing an infinite number of conjectures stronger/stricter than GC. VGC has great potential importance in the optimization of the GC experimental verification (including other possible theoretical and practical applications in mathematics and physics). VGC can be also regarded as a very special self-similar property of the distribution of the primes. This present survey contains some new results on VGC.
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