Primes, Pi, and Irrationality Measure

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dc.creatorSondow, Jonathan
dc.date2007-10-09
dc.date.accessioned2026-07-07T08:35:09Z
dc.date.available2026-07-07T08:35:09Z
dc.descriptionA 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 $p_{n+1}$.
dc.description2 pages, submitted for publication
dc.identifierhttps://arxiv.org/abs/0710.1862
dc.identifierhttp://arxiv.org/abs/0710.1862
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/139663
dc.subjectNumber Theory
dc.subjectGeneral Mathematics
dc.subject11N05, 11J82
dc.titlePrimes, Pi, and Irrationality Measure
dc.typetext

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