2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139663A folklore proof of Euclid's theorem on the infinitude of primes uses the Euler product and the irrationality of $ζ(2) = π^2/6$. A quantified form of Euclid's Theorem is Bertrand's postulate $p_{n+1} < 2p_n$. By quantifying the folklore proof using an irrationality measure for $6/π^2$, we give a proof (communicated to Paulo Ribenboim in 2005) of a much weaker upper bound on $p_{n+1}$.2 pages, submitted for publicationNumber TheoryGeneral Mathematics11N05, 11J82text