Chebyshev's theorem

English

Etymology

From Template:W, the discoverer.

Proper noun

1. The theorem that the prime counting function is of the same order of magnitude as x / ln x, i.e., for the prime counting function π, there are positive constants c and C such that:

   $\mathrm{\forall }x\in \mathbb{N}:\frac{cx}{\ln x}<=\pi (x)<=\frac{Cx}{\ln x}$

2. Bertrand's postulate, as proven by Chebyshev.
3. Chebyshev's inequality.