Re: Sum of 1/Primes
- To: mathgroup at smc.vnet.net
- Subject: [mg36951] Re: [mg36910] Sum of 1/Primes
- From: Roberto Brambilla <rlbrambilla at cesi.it>
- Date: Thu, 3 Oct 2002 00:16:29 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
At 03.31 02/10/02 -0400, you 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
>
>
>
Hi Matthias,
The serie is divergent!
I suggest you to look at this beautiful introduction to primes distribution
http://www.maths.ex.ac.uk/%7Emwatkins/zeta/vardi.html
Bye, rob
Roberto Brambilla
CESI
Via Rubattino 54
20134 Milano
tel +39.02.2125.5875
fax +39.02.2125.5492
rlbrambilla at cesi.it