The Fundamental Theorem of Arithmetic proves that the infinite (hereinafter ∞) natural numbers are primes or compounds and are the producer of prime numbers; satisfying the two versions of Goldbach’s conjecture will allow us to prove that even ∞ natural numbers are the sum of 2 prime numbers, ∞ odd numbers are the sum of only 3 prime numbers; satisfying Euclid’s twin primes conjecture allows us to give a solution to the strong version of Goldbach’s conjecture, "all even ∞ are the sum of two primes" by not looking for the impossible combinatorics between two primes whose quantity and value we do not know , but analyzing the distances between two consecutive prime numbers spaced only by the multiple numbers.