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MathGroup Archive 2002

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Re: Sum of 1/Primes

  • To: mathgroup at smc.vnet.net
  • Subject: [mg36946] Re: [mg36910] Sum of 1/Primes
  • From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
  • Date: Thu, 3 Oct 2002 00:16:21 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

The fact that  Sum[1/Prime[n], {n, 1,Infinity}]==Infinity is a rather 
famous theorem of  Euler. It implies that there must be infinitely many 
primes (otherwise the sum would be finite), and was the beginning of a 
vast area of mathematics, which includes such concepts as Dirichlet 
series, Riemann's zeta function etc.

Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/


On Wednesday, October 2, 2002, at 04:31 PM, 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
>
>
>
>



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