Bertrand postulate

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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).


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