2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126174We note that the inequalities $0.92 \frac{x}{\log(x)} <π(x)< 1.11 \frac{x}{\log(x)}$ do not hold for all $x\ge 30$, contrary to some references. These estimates on $π(x)$ came up recently in papers on algebraic number theory.Number Theory11N05text