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MathGroup Archive 2005

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Re: Special Prime Product

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53420] Re: Special Prime Product
  • From: "Gilmar" <gilmar.rodriguez at nwfwmd.state.fl.us>
  • Date: Tue, 11 Jan 2005 01:30:58 -0500 (EST)
  • References: <cro3ga$hgo$1@smc.vnet.net><crt2na$ejv$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Dear Mathematica Help Group:

Thank you for your wonderful comments and suggestions.

I'm basically following the beautiful article entitled:

"Evidence for Goldbach" appearing in the following web site:

http://www.mathpages.com/home/kmath101.htm

After building the first plot (please, download the following notebook:

http://www.gilmarlily.netfirms.com/download/Evidence_for_Goldbach.nb

), I'm now attempting to build the second plot appearing at the bottom
of the article.  That plot depicts:

k[n_] := Log[F[n]]/Log[n]

where

(1.) F[n_]:= f[n]*Special Prime Product,

(2.) f[n_] := Block[{i, t = 0}, For[i = 1,
Prime[i] <= Floor[n/2], ++i, If[PrimeQ[n - Prime[i]], ++t]]; t]

and

(3.) n is even, and equal or greater than 4.

Any further comments that you might have after reading the above, will
be also most welcome.

Grateful to you all:

Gilmar Rodriguez Pierluissi


Paul Abbott wrote:
> In article <cro3ga$hgo$1 at smc.vnet.net>,
>  "Gilmar" <gilmar.rodriguez at nwfwmd.state.fl.us> wrote:
>
> > I'm attempting to form a product:
> > _____
> > |  | (p-2)
> > |  | -------
> > |  | (p-1)
> > p Prime, p|n
> >
> > I call the program:
> >
> > << NumberTheory`NumberTheoryFunctions`
> > and use the function "PrimeFactorList" in it,  to build
> > the following module:
> >
> > specpriprod[n_]:=
> >
Module[{v},v=Product[(primeFactorList[n][[i]]-2)/(primeFactorList[n][[i]]-2),
> > {i,Length[PrimeFactorList[n]]}];v]
> >
> > specpriprod is an abbreviation for "Special Prime Product".
> >
> > When I evaluate:
> > Table[{n,specprimprod[n]},{n,4,100,2}]
> >
> > I only get specprimprod[n] = 0 for n even between 4 and 100.
> > Help! and Thank you for your help!
> >
>
> Others have pointed out the error in your code. I would just like to
add
> that at
>
>   http://mathworld.wolfram.com/PrimeProducts.html
>
> you will find some relevant formulas along with a downloadable
> Mathematica Notebook.
>
> Cheers,
> Paul
>
> --
> Paul Abbott                                   Phone: +61 8 6488 2734
> School of Physics, M013                         Fax: +61 8 6488 1014
> The University of Western Australia      (CRICOS Provider No 00126G)

> 35 Stirling Highway
> Crawley WA 6009                      mailto:paul at physics.uwa.edu.au
> AUSTRALIA                            http://physics.uwa.edu.au/~paul


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