Some information-theoretic computations related to the distribution of prime numbers
Abstract
Description
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.
10 pages; see also http://pages.cs.aueb.gr/users/yiannisk/
10 pages; see also http://pages.cs.aueb.gr/users/yiannisk/