When Andrew Wiles proved FLT, all he needed to do was to prove "semi-stable elliptic curve case" of Shimura-Taniyama conjecture. He did not need to start from scratch, he just needed to fill this crucial important "missing gap" ?
Is there a similar conjecture (or "missing gap" or "missing links") for Goldbach Conjecture ? If this conjecture is proved, then Goldbach Conjecture is proved.
Can anyone point some directions ?
Maybe there are many such conjectures. Is there any recent summary ?