International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 1, Pages 75-85
doi:10.1155/S0161171296000129
Further results on a generalization of Bertrand's postulate
Department of Mathematics, Physics and Computer Science, Ryerson Polytechnic University, Ontario, Toronto M5B 2K3, Canada
Received 6 November 1992; Revised 28 February 1995
Copyright © 1996 George Giordano. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Let d(k) be defined as the least positive integer n for which pn+1<2pn−k. In this paper we will show that for k≥286664, then d(k)<k/(logk−2.531) and for k≥2, then k(1−1/logk)/logk<d(k). Furthermore, for k sufficiently large we establish upper and lower bounds for d(k).