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This is the Prime Pages'
interface to our BibTeX database. Rather than being an exhaustive database,
it just lists the references we cite on these pages. Please let me know of any errors you notice.References: [ Home  Author index  Key index  Search ]
 Dusart99
 P. Dusart, "The k^{th} prime is greater than k(ln k+ln ln k1) for k> 2," Math. Comp., 68:225 (January 1999) 411415. MR 99d:11133
Abstract:
Rosser and Schoenfeld have use the fact that the first 3,500,000 zeros of the Riemann zeta function lie on the critical line to give estimates on ψ(x) and θ(x). With an improvement of the above result by Brent et. al., we are able to improve these estimates and to show that the k^{th} prime is greater than k(ln k + ln ln k 1) for k ≥ 2. We give further results without proof.
