2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142541We study large partial sums, localized with respect to the sums of variances, of a sequence of centered random variables. An application is given to the distribution of prime factors of typical integers.8 pages; small changes suggested by the referee. To appear in Stat. Prob. LettersProbabilityNumber Theory60G50; 11N25text