# Bertrand postulate

From Encyclopedia of Mathematics

For any natural number $n>3$ there exists a prime number that is larger than $n$ and smaller than $2n-2$. In its weaker formulation Bertrand's postulate states that for any $x>1$ there exists a prime number in the interval $(x, 2x)$. The postulate was advanced by J. Bertrand in 1845 on the strength of tabulated data, and was proved by P.L. Chebyshev (cf. Chebyshev theorems on prime numbers).

#### References

[1] | P.L. Chebyshev, "Oeuvres de P.L. Tchebycheff" , 1 , Chelsea, reprint (1961) (Translated from Russian) |

[a1] | G.H. Hardy, E.M. Wright, "An introduction to the theory of numbers" , Clarendon Press (1965) pp. 343ff |

**How to Cite This Entry:**

Bertrand postulate.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Bertrand_postulate&oldid=53756

This article was adapted from an original article by B.M. Bredikhin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article