Has there been any research into the structure of a non-Goldbach number? This seems like it would be a profitable area for proof by contradiction, so I assume that someone has already done it. (i.e. either the structure proves impossible, or it would allow one to calculate a non-goldbach number)
If so, I'd be interested in sampling some of it. I have googled and turned up nothing, hence this question.
(Apologies if this question is at the wrong level for this site).