与素数分布有关的信息论计算
Some information-theoretic computations related to the distribution of prime numbers
摘要：
我们说明了如何基本的信息理论的想法可能被用来提供证明著名的，非平凡的结果在数论。具体来说，我们给出了一个基本的和相当短的证明以下渐近结果：（log p）/p的总和，采取了所有素数p不超过n，是渐近对数n的n趋于无穷大。我们也给有限n界精炼上述限制。这个结果最初由切比雪夫在1852年证明，与著名的素数定理密切相关。
英文摘要：
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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