I have the following conjecture in regard to Goldbach's Conjecture which I have found via my own experimentation. I wanted to run it by here to see if it is correct and can be proved formally.
$\forall$ N $\ge$ 20 s.t. N is even we define the set A(N) as
$$ A(N)=\{(a,b,c)\ |\ a<b<c<N\ s.t. (a,b,c)\ is\ a\ prime\ triplet\} $$
We also define the set B(N) as:
$$ B(N)=\{c\ |\ \forall(a,b,c)\in A(N)\}$$
Then $\exists\ c\in B(N)$ s.t.
$$ c\ and\ N-c\ are\ prime$$
Please do let me know what you think about this. I have programmatically verified it till $10^9$ and am working on testing it for larger numbers. However, I am unable to prove/disprove this mathematically.