Research Repository

A Note on Short Intervals Containing Primes

Hassani, Mehdi and Sariolgalam, Narges (2004) A Note on Short Intervals Containing Primes. Research report collection, 7 (3).

[img] Text
interval.pdf

Download (119kB)

Abstract

In 1999, P. Dusart showed that for x ≥ 3275, there exists at least a prime number in the interval (x, x(1 + 1/(2ln²x))] and in 2003, O. Ramaré and Y. Saouter showed that for x ≥ 10726905041 there exists at least a prime number in the interval (x(1 − ∆⁻¹), x], in which ∆ = 28314000. In this note, we show that for x ≥ 1.17×10¹⁶³⁴, we can yield Ramaré-Saouter’s result from Dusart’s result.

Item Type: Article
Uncontrolled Keywords: primes
Subjects: FOR Classification > 0101 Pure Mathematics
Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Depositing User: Research Group in Mathematical Inequalities and Applications
Date Deposited: 18 Jul 2012 23:43
Last Modified: 23 May 2013 16:54
URI: http://vuir.vu.edu.au/id/eprint/18050
ePrint Statistics: View download statistics for this item

Repository staff only

View Item View Item

Search Google Scholar