2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/214683This note discusses the existence of prime numbers in short intervals. An unconditional elementary argument seems to prove the existence of primes in the short intervals [x, x + y], where y >= x^(1/2)(log x)^e, e > 0, and a sufficiently large number x > 0. Further, an extension of Bertrand's postulate to arithmetic progressions will be considered31 PagesGeneral Mathematics11A41, 11N05, and 11M26text