Legendre's constant

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In mathematics, Legendre's constant is a "phantom" that does not really exist.

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

<math>\pi(n) = {n \over \ln(n) - A(n)}</math>

where

<math>\lim_{n \rightarrow \infty } A(n) \approx 1.08366\dots .</math>

The quantity 1.08366... was called Legendre's constant. Later Carl Friedrich 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 constantfr:Constante de Legendre pl:Stała Legendre'a