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**1 - 2**of**2**### Some Information-Theoretic Computations Related to the Distribution of Prime Numbers

, 2007

"... 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, p≤n log p p ∼ log n, as n → ∞, where the sum is over all prim ..."

Abstract
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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, p≤n log p p ∼ log n, as n → ∞, where the sum is over all primes p not exceeding n. 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.

### Some Information-Theoretic Computations . . .

- SUBMITTED TO JORMA RISSANEN’S FESTSCHRIFT VOLUME
, 2008

"... 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, p≤n log p p ∼ log n, as n → ∞, where the sum is over all prim ..."

Abstract
- Add to MetaCart

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, p≤n log p p ∼ log n, as n → ∞, where the sum is over all primes p not exceeding n. 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.