Chebyshev's theorem

From Pafnuty Chebyshev, the discoverer.

Chebyshev's theorem

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:

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

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