2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64414Goldston and Montgomery [3] proved that the Strong Pair Correlation Conjecture and two second moments of primes in short intervals are equivalent to each other under Riemann Hypothesis. In this paper, we get the second main terms for each of the above and show that they are almost equivalent to each other.Number Theory11M26;11N05text