2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66025Differentiable real function reproducing primes up to a given number and having a differentiable inverse function is constructed. This inverse function is compared with the Riemann-Von Mangoldt exact expression for the number of primes not exceeding a given value. Software for computation of the direct and inverse functions and their derivatives is developed. Examples of approximate solution of Diophantine equations on the primes are given.28 pages, 9 figures, 1 Fortran packages included in source, 2 listings with solutions of Diophantine equations on primes and twinsNumber Theory11N05, 11M20, 65D07text