From Wikipedia :
Goldbach' s conjecture is one of the oldest and best - known unsolved problems in number theory and all of mathematics . It states that every even natural number greater than 2 is the sum of two prime numbers . The conjecture has been shown to hold for all natural numbers less than 4*1018, but remains unproven despite considerable effort .
Resolve @ ForAll[n, {EvenQ[n], IntegerQ[i], IntegerQ[j], n > 2}, n == Prime[i] + Prime[j]]
True
