Science Fair Project Encyclopedia

Science Fair Project Encyclopedia Contents Page

Legendre's constant

Legendre's constant is a "phantom" that doesn't really exist.

Before the discovery of the prime number theorem, examination of available numerical evidence for known primes had led Legendre to conjecture that perhaps

$\pi(n) = {n \over \ln(n) - A(n)}$

where

$\lim_{n \rightarrow \infty } A(n) \approx 1.08366\dots .$

The quantity 1.08366... was called Legendre's constant. Later Gauss also examined the numerical evidence and concluded that the limit might be lower. In fact, the best limit value of A(n) turns out to be 1. Thus, there is no "Legendre's constant".

External link

MathWorld: Legendre's constant

Categories: Number theory

Last updated: 05-23-2005 07:16:33

Science Fair Project Encyclopedia Contents Page

10-26-2009 08:16:03
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details

All Science Fair Projects