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MathGroup Archive 2003

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Re: Summations with Primes

  • To: mathgroup at smc.vnet.net
  • Subject: [mg39988] Re: Summations with Primes
  • From: Bill Rowe <listuser at earthlink.net>
  • Date: Thu, 13 Mar 2003 03:06:33 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On 3/12/03 at 2:29 AM, afelder at crsi.org (Anthony Felder) wrote:

>Can you tell me if, when calculating a summation of f(i) where i goes
>from imin to imax, Mathematica can be forced to only use prime values
>for i?

Yes, by adding the appropriate code. That is there isn't a built in directive to do what you want.

I think there are two basic approaches. First would be to generate a list of primes, map f to the elements of that list then sum. For example:

Tr[f/@Select[Range[imin, imax], PrimeQ]] will do the trick

This approach might be made more efficient using the NextPrime function in the package NumberTheory`NumberTheoryFunctions`

The other approach would be to modify f so that it returned zero for non-prime arguments. I think this approach is likely to be slower than the first approach.


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