Gödel proved that there are true sentences that cannot be proved.

Suppose I told you that the Goldbach conjecture is one of those. (The Goldbach conjecture supposes that every even integer number can be expressed as the sum of two odd primes.)

Is that logically possible? (And, no, I haven't proved it!)

The real Goldbach conjecture supposes that every integer number can be expressed as the sumo f any prime, not just odd primes. Also, Goldbach considered the number 1 to be a prime.

This information might be helpful to some people who have made comments about 4, being an exception to the Goldbach conjecture.