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MathGroup Archive 2005

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strange errors for numerical evaluation of an infinite sum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58322] strange errors for numerical evaluation of an infinite sum
  • From: Roger Bagula <rlbagulatftn at yahoo.com>
  • Date: Tue, 28 Jun 2005 05:13:23 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

The Sum is:
aa = Sum[1/(Prime[n + 1] - Prime[n])^PrimePi[n], {n, 1, Infinity}]
The numerical evaluation is:
N[aa]

The error is:
\!\(\*
   RowBox[{\(Prime::"intpp"\), \(\(:\)\(\ \)\), "\<\"Positive integer 
argument
       expected in \\!\\(
       Prime[16.`]\\). \\!\\(\\*ButtonBox[\\\"More?\\\", \
ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \
ButtonData:>\\\"Prime::intpp\\\"]\\)\"\>"}]\)

and:

\!\(\*
   RowBox[{\(General::"stop"\), \(\(:\)\(\ \)\), "\<\"Further output
     of \\!\\(Prime :: \\\"intpp\\\"\\) will be suppressed during this \
calculation. \\!\\(\\*ButtonBox[\\\"More?\\\", \
ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \
ButtonData:>\\\"General::stop\\\"]\\)\"\>"}]\)

I got a slightly better answer by extending: $MaxExtraPrescision
but I'm only getting a number to 19 places , it appears.

Any help will be appreciated. It seem to be some kind of frequency 
number associated with the Primes.
I don't know if it is a new constant or not.

Respectfully,
Roger L. Bagula


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