Abstract. We outline a proof that if the Generalized Riemann Hypothesis holds, then every odd number above 5 is a sum of three prime numbers. The proof involves an asymptotic theorem covering all but a finite number of cases, an intermediate lemma, and an extensive computation. 1.

It is shown that if every odd integer n> 5 is the sum of three primes, then every even integer n> 2 is the sum of two primes. A conditional proof of Goldbach’s conjecture, based on Cramér’s conjecture, is presented. Theoretical and experimental results available on Goldbach’s conjecture allow that a less restrictive conjecture than Cramér’s conjecture be used in the conditional proof. A basic result of the Maier’s paper on Cramér’s model is criticized. 1