Abstract
Goldbach's conjecture is important because it suggests a causal relationship between all the positive even numbers ( ≥ 4) and the sums of the primes. In this paper, we prove that the sum of any two odd prime numbers is an even number and thereby the sequence of all even numbers > 4 can be expressed as the sum of two odd primes ad infinitum (Goldbach's strong conjecture). And that every even number > 6 can be written as the sum of two odd primes plus 2, which in turn implies that every odd number ≥ 9 can be expressed as the sum of exactly two odd primes plus 3 (i.e. three odd primes) (Goldbach's weak conjecture).