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

Ioannis Kontoyiannis

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arXiv · 0710.4076

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

Ioannis Kontoyiannis

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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.

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Ioannis Kontoyiannis. 2007-11-06. Some information-theoretic computations related to the distribution of prime numbers. https://arxiv.org/abs/0710.4076

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