Some information-theoretic computations related to the distribution of prime numbers
| dc.creator | Kontoyiannis, Ioannis | |
| dc.date | 2007-10-22 | |
| dc.date | 2007-11-06 | |
| dc.date.accessioned | 2026-07-07T08:40:25Z | |
| dc.date.available | 2026-07-07T08:40:25Z | |
| dc.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. | |
| dc.description | 10 pages; see also http://pages.cs.aueb.gr/users/yiannisk/ | |
| dc.identifier | https://arxiv.org/abs/0710.4076 | |
| dc.identifier | http://arxiv.org/abs/0710.4076 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141369 | |
| dc.subject | Information Theory | |
| dc.subject | Number Theory | |
| dc.subject | Probability | |
| dc.title | Some information-theoretic computations related to the distribution of prime numbers | |
| dc.type | text |