I thought that maybe the most brilliant brains around here (Kedaman and Guv, of course ) might have an idea of how to start trying to prove (or refute) Goldbach's Conjecture.

As you all know (or maybe not), the conjecture says:

"Every even number bigger than 2, can be represented by the sum of 2 prime numbers"

For those who never heard of this hypothesis, it's one of the most difficult unsolved problems in the whole math!

I believe we (I mean, the humanity) don't know enough about the prime numbers.

For example, there is no formula which tells us the next prime number when we give it a certain prime number.

We cannot know exactly the amount of prime numbers below a given number.

Of course there are several theorems and facts we do know about the prime numbers, but it doesn't seem enough for solving Goldbach's conjecture.

Any suggestions/Comments?

P.S: Goldbach's conjecture was proved to be true up to 10^15, and counting...