2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72080We introduce Wilson's theorem and Clement's result and present a necessary and sufficient condition for p and p+2k to be primes where k is a positive integer. By using Simiov's Theorem, we derive an improved version of Clement's result and characterizations of Polignac twin primes which parallel previous characterizations.8 pagesNumber Theory11A41; 11A51text