2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224972In this work we consider sums of primes that converging very slow. We set as a base, a reformulation of analytic prime number theorem and we use the values of Riemann Zeta function for the approximation. We also give the truncation error of these approximationsNumber Theory11A41; 11L20; 11Y60text