A Glorious Beginning: Bertrand’s Postulate

Letd(k)be defined as the least positive integernfor whichpn+1<2pn−k. In this paper we will show that fork≥286664, thend(k)<k/(logk−2.531)and fork≥2, thenk(1−1/logk)/logk<d(k). Furthermore, forksufficiently large we establish upper and lower bounds ford(k).

Download Full-text

The Discriminator (A Simple Application of Bertrand's Postulate)

American Mathematical Monthly ◽

10.1080/00029890.1985.11971598 ◽

1985 ◽

Vol 92 (4) ◽

pp. 275-277 ◽

Cited By ~ 4

Author(s):

L. K. Arnold ◽

S. J. Benkoski ◽

B. J. McCabe

Keyword(s):

Simple Application ◽

Bertrand’S Postulate

Download Full-text

Calculations for Bertrand's Postulate

Mathematics Magazine ◽

10.1080/0025570x.1981.11976890 ◽

1981 ◽

Vol 54 (1) ◽

pp. 33-34 ◽

Cited By ~ 4

Author(s):

Heiko Harborth ◽

Arnfried Kemnitz

Keyword(s):

Bertrand’S Postulate

Download Full-text

A stronger Bertrand’s postulate with an application to partitions

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1972-0292746-6 ◽

1972 ◽

Vol 33 (2) ◽

pp. 226-226

Author(s):

Robert E. Dressler

Keyword(s):

Bertrand’S Postulate

Download Full-text

The generalization and proof of Bertrand's postulate

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171287000917 ◽

1987 ◽

Vol 10 (4) ◽

pp. 821-823 ◽

Cited By ~ 1

Author(s):

George Giordano

Keyword(s):

Lower Bounds ◽

Upper And Lower Bounds ◽

Bertrand’S Postulate

The purpose of this paper is to show that for0<r<1one can determine explicitly anx0such that∀x≥x0,∃at least one prime betweenrxandx. This is a generalization of Bertrand's Postulate. Furthermore, the same procedures are used to show that if one can find upper and lower bounds forθ(x)whose difference iskxρthen∃a prime betweenxandx−Kxρ, wherek,K>0are constants,0<ρ<1andθ(x)=∑p≤xlnp, wherepruns over the primes.

Download Full-text