The main idea of this article lies in the fact that Goldbach's strong conjecture is associated with the progression ofnatural integers from 0 to infinity, which results in precise gaps between prime numbers. The gap of 6 is the mostregular between primes 6x + 1 on the one hand and primes 6x — 1 on the other. In this article, using the equations 3x ± 5and analyzing the 6-based gaps between primes while determining the initial conditions that make a prime appear afteror before an integer, this article argues for the truth of Goldbach's strong conjecture. Two new concepts are introducedfor the first time : Goldbach's gap and Goldbach's transposition. By analyzing its key digits (units and tens), a primenumber itself can lead to the conversion of an even number into two primes. A new algorithm is deduced from theseresults, enabling us to locate prime numbers located at equal distance from any integer, even or odd, prime orcomposite. This constitutes a decisive proof of Goldbach's strong conjecture, since it means that any even number canbe converted into the sum of two prime numbers.