Chebyshev's theorem

Chebyshev's theorem

English

Etymology

From Pafnuty Chebyshev, the discoverer.

Proper noun

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.