View source for Bertrand postulate

For any natural number <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015810/b0158101.png" /> there exists a [[Prime number|prime number]] that is larger than <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015810/b0158102.png" /> and smaller than <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015810/b0158103.png" />. In its weaker formulation Bertrand's postulate states that for any <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015810/b0158104.png" /> there exists a prime number in the interval <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b015/b015810/b0158105.png" />. 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|Chebyshev theorems on prime numbers]]).

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  P.L. Chebyshev,   "Oeuvres de P.L. Tchebycheff" , '''1''' , Chelsea, reprint  (1961)  (Translated from Russian)</TD></TR></table>



====Comments====


====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  G.H. Hardy,   E.M. Wright,   "An introduction to the theory of numbers" , Clarendon Press  (1965)  pp. 343ff</TD></TR></table>