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 alre …

EDIT : I copy-paste the beginning of a previous question since Gerry Myerson suggested this question should be self-contained. "let's consider a composite natural number $n$ great …

On leafing through some papers of John Nash (available online on his webpage) I found this intriguing little observation: Noticing that with larger even numbers it seemed to be …

Let $n \in \mathbb{N}, n \geq 2$. By minimal Goldbach basis $G_{2n}$(if it is nonempty) of $2n$ , I mean the minimal set of primes such that every even number less than or equal to …

I have been reading a paper on the Goldbach conjecture found at http://people.exeter.ac.uk/pt224/Goldbach.pdf. At one point, the author (Paul Truman), states: Let $z=N^{1/8}$, the …