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MathGroup Archive 2002

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Re: Sum of 1/Primes

  • To: mathgroup at smc.vnet.net
  • Subject: [mg36952] Re: Sum of 1/Primes
  • From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
  • Date: Thu, 3 Oct 2002 00:16:32 -0400 (EDT)
  • References: <ane7i5$ka7$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Matthias.Bode at oppenheim.de wrote:
> 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.

The latter. It is a well known fact that the series diverges (which, by
the way, shows that there are infinitely many primes  :-).

David

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