Conjectura Forte de Goldbach Derivada da Conjectura de MariltonCR dos Primos Encaixados

Arithmetic–Combinatorial Extension (v4) In the next version, the theory of "nested primes" will be expanded to include all numbers, positive and negative, while preserving the non-marking logic that identifies prime candidates. This expansion reveals an arithmetic symmetry between positive and negative blocks that, for any even number m, guarantees the existence of a perfect pair (k,m−k) of non-marked numbers—and therefore primes—whose sum is exactly m. This new perspective brings the combinatorial structure of the theory closer than ever to one of the greatest challenges in mathematics: the Goldbach Conjecture. Example of Valid and Invalid Pairs Consider the block K40(0)={1,…,40} and its mirrored block K40(−1)={−39,…,0}. Our goal is to find pairs of "non-marked" (prime) numbers, one from each block, that sum to 40. Invalid Candidate: The number 7 Let's analyze the number 7, which is prime. Its complement that sums to 40 is 33. However, 33 is divisible by 3 and 11, which means it is a composite number and thus "marked." Since one element of the pair (7,33) is marked, the pair is invalid. This demonstrates that even if a number is prime in the positive block, its complement may not be. Valid Candidate: The number 3 Now, let's analyze the number 3. Its complement that sums to 40 is 37. The number 3 is a prime, non-marked number. To check if 37 is prime, we test its divisibility by numbers less than srq(37)<7. It is not divisible by 2, 3, or 5. Therefore, 37 is also prime and non-marked. Both elements of the pair (3,37) are prime, making it a valid pair. Central Idea This example illustrates a crucial point: when extending the analysis to mirrored blocks, it's not enough for a number to be prime in the positive block. Its corresponding complement in the negative block must also be prime for the pair to be considered valid. The number 7 fails this test, while 3 is a successful example. A concise explanation of the proposed proof of the Strong Goldbach Conjecture The proof builds upon the structural framework established by the MariltonCR Conjecture of Fitted Primes.It demonstrates that, within specific evenly spaced intervals—formed by systematically eliminating numbers divisible by small divisors—there is always at least one number that remains unmarked.Such numbers are coprime with all integers in [2,m][2, m] and, therefore, prime candidates. To apply this to Goldbach’s Conjecture, an even number mm is represented symmetrically as: P1=[1,m],P0=[1−m,0]P_1 = [1, m], \quad P_0 = [1 - m, 0] Every pair (p,m−p)(p, m - p) formed from these sets sums to mm.However, a prime p∈P1p \in P_1 is valid only if it is coprime with all integers in [2,m][2, m] except itself.Non-coprime primes are systematically removed by the divisibility pattern described in the MariltonCR Limits of Marking Repetition Theorem. The key mechanism is that the repetition of divisor markings—both forward and backward along the number line—guarantees at least one unmarked position on each side of the symmetry.This position corresponds to a prime in P1P_1 whose complement in P0P_0 is also prime, thereby satisfying m=p+p′m = p + p' for all even m>2m > 2, assuming the conjecture holds. 📎 Full proof available at:https://doi.org/10.5281/zenodo.16734582