Prove that every even integer greater than 2 can be expressed as the sum of two prime numbers.
This statement is known as the Goldbach Conjecture, which was first proposed by Christian Goldbach in 1742. Although it has been tested extensively for even integers up to very large values and found to be true in those cases, a general proof for all even integers greater than 2 has not yet been discovered. Thus, I cannot provide a definitive proof for this conjecture.