Numerical evidence in favor of the Arenstorf formula

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71442The formula $\lim_{N\to\infty}\sum_{p<N,p,p+2 both prime} \log(p)\log(p+2) = C_2$ is tested on the computer up to $N=2^{40}\approx 1.1\times 10^{12}$ and very good agreement is found.Number TheoryNumerical evidence in favor of the Arenstorf formulatext