The kth prime is greater than k(ln k+ln ln k-1) for k≥2
Abstract
Rosser and Schoenfeld have used the fact that the first 3,500,000 zeros of the Riemann zeta function lie on the critical line to give estimates on psi(x) and theta(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.
- Publication:
-
Mathematics of Computation
- Pub Date:
- 1999
- Bibcode:
- 1999MaCom..68..411D