This paper investigates Goldbach's Conjecture using a novel exploratory algorithm. We derive a function from this algorithm that exhibits a critical point at the midpoint of even numbers. Empirical testing suggests a correlation between prime numbers near this midpoint and Goldbach decompositions generated by the algorithm. Furthermore, we explore the conceptual connections between this "sweet spot" and the regularity in prime distribution anticipated by the Riemann Hypothesis. We posit that the observed relationship between Goldbach summands around the mean may reflect the underlying order that the Riemann Hypothesis seeks to elucidate.