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Re: Sum of 1/Primes

• To: mathgroup at smc.vnet.net
• Subject: [mg36955] Re: [mg36910] Sum of 1/Primes
• From: Murray Eisenberg <murraye at attbi.com>
• Date: Thu, 3 Oct 2002 00:16:39 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200210020731.DAA20623@smc.vnet.net>
• Reply-to: murray at math.umass.edu
• Sender: owner-wri-mathgroup at wolfram.com

It is well known that the infinite series of reciprocals of the primes 
DIVERGES!

See, for example:

   http://www.utm.edu/research/primes/infinity.shtml


Matthias.Bode at oppenheim.de wrote:
> Dear Colleagues,
> 
> I calculated:
> 
> Sum[1/Prime[n], {n, 15000}] // N
> 
> Result: 2.74716
> 
> Now I wonder if this sum will converge or keep on growing, albeit very
> slowly.
> 
> Best regards,
> 
> Matthias Bode
> Sal. Oppenheim jr. & Cie. KGaA
> Koenigsberger Strasse 29
> D-60487 Frankfurt am Main
> GERMANY
> Tel.: +49(0)69 71 34 53 80
> Mobile: +49(0)172 6 74 95 77
> Fax: +49(0)69 71 34 95 380
> E-mail: matthias.bode at oppenheim.de
> Internet: http://www.oppenheim.de
> 
> 
> 
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street
Amherst, MA 01375

• References:
  • Sum of 1/Primes
    • From: Matthias.Bode@oppenheim.de