There are at least two theorems known as Chebyshev's theorem.

The first is Bertrand's postulate, proposed by Bertrand in 1845 and proved by Chebyshev using elementary methods in 1850 (Derbyshire 2004, p. 124).

The second is a weak form of the prime number theorem stating that the order of magnitude of the prime counting function is

where denotes "is asymptotic to" (Hardy and Wright 1979, p. 9). More precisely, Chebyshev showed in 1849 that if

for some constant C, then C = 1 (Derbyshire 2004, p. 123).

In 1850, Chebyshev also showed that cannot differ from by more than approximately 10% (Derbyshire 2004, p. 124).

Bertrand's Postulate, Prime Counting Function, Prime Number Theorem