2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128207We consider the regular parts for basic functions of prime numbers with Riemann approximation accuracy.8 pages, 2nd version after major revision. Formula (5) in 1st version is the simplified form of (12). For the regular part of R(x)-function only the first term was considered in formula (5)Number Theory11N05; 11A41text