I’m a Pediatrician specialist and hobbyist in mathematics: however, I’ve manage to publish a generalization of GC (as applied on primes with prime indexes of any order) in both a peer-review journal and as an independently verified reference of two sequences submitted on OEIS in 2017 and 2018.

Maybe my generalized Goldbach conjecture (aka VBGC) (which is a meta-conjecture and the only published meta-conjecture on primes from my knowledge) will inspire professional mathematicians on this forum to find new strategies in demonstrating GC.

https://www.vixrapedia.org/wiki/VBGC (which is the shortest possible introduction on VBGC)

http://www.sciencedomain.org/abstract/21625

https://www.researchgate.net/publication/320740914

https://books.google.ro/books?id=tvdODwAAQBAJ

See also the VBGC-based integer sequences on OEIS (which were approved in 2017 and 2018 after VBGC review with 2 distinct software: Mathematica and PARI, plus Visual C in which I’ve tested it personally):

http://oeis.org/A316460

https://oeis.org/A282251

As an additional note (see VBGC reference), VBGC can be considered an indirect „proof” of BGC, because VBGC essentially states/conjectures an infinite set of finite values f(a, b) (above which all even numbers can be written as the sum of two distinct prime-index primes of any finite order) which indicates that BGC (equivalent to VBGC (0,0)) is very probably true, because f(0,0) is only a special case (the first one) of this (conjectured) infinite set. In other (more plastic) words, BGC is just a “tree” in the plausibly infinite VBGC “wood”, which VBGC is a spectacular quasi-fractal property of primes distribution (Dp) when applied iteratively on itself (and holding VBGC).

VBGC supports even more improvements (which will be contained in a future article on VBGC which is in working progress)

dr. Andrei-Lucian Dragoi,

http://www.dragoii.com