I think Goldbach's conjecture is quite well-know at this point, but there is no problem restating it: any even integer greater than $2$ can be written as the sum of two prime numbers.
But what about distinct prime numbers? For every even integer $n$ that does not equal $2p$, for $p$ a prime, Goldbach's conjecture obviously implies that $n$ can be written as the sum of two distinct prime numbers, but the question in the title remains: what if $n=2p$? (Ignore $p=3$, which clearly fails...)
I tested all prime numbers up to 10.000.000 and found no exceptions.