2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158058Let βbe a real number. Then for almost all irrational α>0 (in the sense of Lebesgue measure) \limsup_{x\to\infty}π_{α,β}^*(x)(\log x)^2/x>=1, where π_{α,β}^*(x)={p<=x: both p and [αp+β] are primes}.Number Theory11N05 (Primary); 11N36, 11P32 (Secondary)text