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

Kontoyiannis, I (2008) Some information-theoretic computations related to the distribution of prime numbers. In: Festschrift in Honor of Jorma Rissanen. UNSPECIFIED.

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Abstract

We 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.

Item Type: Book Section
Uncontrolled Keywords: cs.IT cs.IT math.IT math.NT math.PR
Subjects: UNSPECIFIED
Divisions: Div F > Signal Processing and Communications
Depositing User: Cron Job
Date Deposited: 08 Jan 2018 20:12
Last Modified: 18 Aug 2020 12:42
DOI: