A Representation of Prime Gaps by Signed Sums of Primes

Representação de lacunas entre números primos por meio da soma de números primos com sinal. Resumo. Abstract. This work presents a systematic representation of every even gap between consecutive primes as a signed sum of small primes. The fundamental structure is $g = -1 + c$, where $c = g + 1$ is an odd integer (the "odd core") reached by a signed sum of odd primes. The representation is catalogued by a "calculation memory" m, which satisfies the universal identity $m = g/2$. The catalogue is verified computationally over 719,440 consecutive prime gaps, covering primes up to approximately 719,000. The empirical results confirm the distribution predicted by the Hardy–Littlewood conjecture, notably the equivalence between gaps 2 and 4 and the dominance of gaps that are multiples of 6.