The Goldbach Conjecture - An Emergence Effect of the Primes

The present paper shows that a principle known as emergence lies beneath the strong Goldbach conjecture. Whereas the traditional approaches focus on the control over the distribution of the primes by means of circle method and sieve theory, we give a proof of the conjecture that involves the constructive properties of the prime numbers, reflecting their multiplicative character within the natural numbers. With an equivalent but more convenient form of the conjecture in mind, we create a structure on the natural numbers which is based on the prime factorization. Then, we realize that the characteristics of this structure immediately imply the conjecture and an even strengthened form of it. Moreover, we can achieve further results by generalizing the structuring. Thus, it turns out that the statement of the strong Goldbach conjecture is the special case of a general principle.