From: "Yves Gallot" Subject: Re: Upper bound for the n-th prime number Date: Tue, 19 Jan 1999 00:08:30 +0100 Newsgroups: sci.math >is there an upper bound for the n-th prime number? >I believe not, but I don't know a proof. >Does anyone know a proof (or an upper bound) ? n(Log n + Log Log n - 3/2) < p_n < n(Log n + Log Log n - 1/2) Rosser & Schoenfeld, Approximate formulas for some prime numbers, Illinois, J. Math. 6 (1962), 64-94. Yves ============================================================================== From: tordm@vanz16.physto.se (Tord G.M. Malmgren) Subject: Re: Upper bound for the n-th prime number Date: 25 Jan 1999 09:36:12 GMT Newsgroups: sci.math In article <78gqrd$4tj$1@cantuc.canterbury.ac.nz>, mathwft@math.canterbury.ac.nz (Bill Taylor) writes: >galloty@wanadoo.fr writes: >>n(Log n + Log Log n - 3/2) < p_n < n(Log n + Log Log n - 1/2) >Is any more known about this? Math. Comp. 68 (1999), pp. 411-415. Tord G M Malmgren | THESE OPINIONS ARE MY OWN, AND NOT OF THIS DEPARTMENT! Stockholm University | e-mail : tordm@physto.se Box 6730 | URL : http://vanh.physto.se/~tordm 113 85 Stockholm | Phone : +46 8 164586 SWEDEN | Fax : +46 8 347817 ============================================================================== From: ribet@math.berkeley.edu (Kenneth A. Ribet) Subject: Re: Bertrand's postulate Date: Mon, 8 Mar 1999 05:48:11 -0800 (PST) Newsgroups: [missing] To: rusin@math.niu.edu Thanks very much for the response. Several people pointed me to a paper by Rosser and Schoenfeld from the 1960s which yields (after some computation) that 5/3 is indeed the largest ratio p_{n+1}/p_n. Best, Ken Ribet