2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128176Green and Tao proved that the primes contains arbitrarily long arithmetic progressions. We show that, essentially the same proof leads to the following result: The primes in an short interval contains many arithmetic progressions of any given length.Number Theory11N13,11B25Arithmetic progressions of primes in short intervalstext