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Re: Re: Summations with Primes

• To: mathgroup at smc.vnet.net
• Subject: [mg40006] Re: [mg39988] Re: Summations with Primes
• From: Kirk Reinholtz <kirk.reinholtz at jpl.nasa.gov>
• Date: Fri, 14 Mar 2003 04:47:39 -0500 (EST)
• References: <200303130806.DAA12131@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Prime/@Range[1,10] will get the first ten primes.

Bill Rowe wrote:
> 
> 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.

• References:
  • Re: Summations with Primes
    • From: Bill Rowe <listuser@earthlink.net>