Some information-theoretic computations related to the distribution of prime numbers

dc.creatorKontoyiannis, Ioannis
dc.date2007-10-22
dc.date2007-11-06
dc.date.accessioned2026-07-07T08:40:25Z
dc.date.available2026-07-07T08:40:25Z
dc.descriptionWe illustrate how elementary information-theoretic ideas may be employed to provide proofs for well-known, nontrivial results in number theory. Specifically, we give an elementary and fairly short proof of the following asymptotic result: The sum of (log p)/p, taken over all primes p not exceeding n, is asymptotic to log n as n tends to infinity. We also give finite-n bounds refining the above limit. This result, originally proved by Chebyshev in 1852, is closely related to the celebrated prime number theorem.
dc.description10 pages; see also http://pages.cs.aueb.gr/users/yiannisk/
dc.identifierhttps://arxiv.org/abs/0710.4076
dc.identifierhttp://arxiv.org/abs/0710.4076
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141369
dc.subjectInformation Theory
dc.subjectNumber Theory
dc.subjectProbability
dc.titleSome information-theoretic computations related to the distribution of prime numbers
dc.typetext

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