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

## 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 |
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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: |