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RE: Sum of 1/Primes

  • To: mathgroup at
  • Subject: [mg36959] RE: [mg36910] Sum of 1/Primes
  • From: David Turner <dturner at>
  • Date: Thu, 3 Oct 2002 00:16:47 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

The sum diverges.  See Elementary Number Theory, 5th edition by David M.
Burton, pages 355-356.

-----Original Message-----
From: Matthias.Bode at [mailto:Matthias.Bode at]
To: mathgroup at
Subject: [mg36959] [mg36910] Sum of 1/Primes

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

Best regards,

Matthias Bode
Sal. Oppenheim jr. & Cie. KGaA
Koenigsberger Strasse 29
D-60487 Frankfurt am Main
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

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