It might be that every even number from 4 up is the sum of two prime numbers. So, can you prove it? Or maybe you found an even number that can't be written as the sum of two prime numbers.
At any rate, the problem attested to by the OP is based upon prime numbers. Primes disturb us since they are only discoverable, but not generative. We cannot answer the assertion until we find out why primes continue to exist in the integers. Why is it that no matter how large the number we calculate up to, we continue finding another prime? Why don't primes disappear once the number gets large enough? That implies a patterning throughout the integers, but such a patterning should be generative, meaning we can generate a prime when needed, and predict them as we go along. This seeming contradiction is behind the reason why primes disturb us.