A Little Problem

Any positive even integer greater than 2 can be expressed as the sum of exactly two prime numbers. It's cool. Try it for yourself.

4 = 2 + 2
6 = 3 + 3
8 = 3 + 5
10 = 5 + 5
...

Two things:
1.) Was I lying before? Can every single one be expressed this way? How about 10234598692032 (or some really big number like that)?

2.) If every single one can be expressed this way, why?

Hm, an extension on Goldbach's conjecture?

It stand for numbers less than 10^9 as tested by computers, but humanity is still unsure for numbers afterwards.

Well, if you want to prove this... Then use the Riemmann Hypothesis, and then find some kind of functional pattern between prime numbers.(has not been done)