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