This article investigates the strong Goldbach conjecture, which states that every even number greater than or equal to four can be written as the sum of two prime numbers. For each even number, the paper introduces a finite sequence built by subtracting the primes smaller than that number from it. The main result shows that this sequence always contains at least one prime term. As a consequence, every even number can be expressed as the sum of two primes. The article also provides the necessary theoretical background, several supporting lemmas, and an algorithm for computing all prime pairs that represent a given even number according to the Goldbach conjecture.
MIHOUBI, Douadi (Fri,) studied this question.