On the estimates of the upper and lower bounds of Ramanujan primes
Abstract
For \(n\ge 1\), the nth Ramanujan prime is defined as the least positive integer \(R_{n}\) such that for all \(x\ge R_{n}\), the interval \((\frac{x}{2}, x]\) has at least n primes. Let \(p_{i}\) be the ith prime and \(R_{n}=p_{s}\). Sondow, Laishram, and other scholars gave a series of upper bounds of s. In this paper we establish several results giving estimates of upper and lower bounds of Ramanujan primes. Using these estimates, we discuss a...
Paper Details
Title
On the estimates of the upper and lower bounds of Ramanujan primes
Published Date
Aug 14, 2015
Journal
Volume
40
Issue
2
Pages
245 - 255
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