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Chebyshev's theorem

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English

Etymology

From Pafnuty Chebyshev, the discoverer

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:
    <math>\forall x\in\mathbb{N}:

\frac{cx}{\ln x} <= \pi(x) <= \frac{Cx}{\ln x}</math>

  1. an alternative name for Bertrand's postulate, as proven by Chebyshev
  2. an alternative name for Chebyshev's inequality

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