The generalization and proof of Bertrand′s postulate

Abstract

ABSTRACT. The purlxse of this paper is to show that for 0 < < one can determine explicitly an x0 such that v x :> Xo, =1 at least one prime between rx and x. This is a generalization of Berwand's Postulate. Furthermore, the same procedures are used to show that if one can find upper and lower bounds for 0(x) whose difference is ', then :q prlrnc