On Goldbach's Conjecture

Abstract

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 Cram\'er's conjecture, is presented. Theoretical and experimental results available on Goldbach's conjecture allow that a less restrictive conjecture than Cram\'er's conjecture be used in the conditional proof. A basic result of the Maier's paper on Cram\'er's model is criticized.