Re: A question about a set-theory approach to minimal Goldbach prime partitions via Mathematica.

*To*: mathgroup at smc.vnet.net*Subject*: [mg55831] Re: [mg55796] A question about a set-theory approach to minimal Goldbach prime partitions via Mathematica.*From*: DrBob <drbob at bigfoot.com>*Date*: Thu, 7 Apr 2005 05:10:11 -0400 (EDT)*References*: <200504060711.DAA13620@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

First of all, having proven that A3 == (n/2 - p)^2, of course you know every A3 is a perfect square (for even n). So the answer to question 1 is YES. (If, by double-strike E, you mean the _positive_ even numbers.) Perhaps you meant to ask whether any of the equivalence classes are empty; that is, whether n/2 - p takes on all possible non-negative integer values. I suspect the answer is yes, but if not, that doesn't affect the conjecture in question 1. Secondly (question 2), finite cases can reveal the failure of such a conjecture, but they can never prove it. Third, PrimeQ[m] is more compact than Element[m, Primes] and directly expresses the test Mathematica will do. In addition, using Break to exit Do is far less clear than a simple While: Clear[areas, brt] brt[n_?EvenQ] /; n > 3 := Block[{m = PrimePi[n/2], p}, While[ !PrimeQ[n - (p = Prime[m])], m--]; p] area[n_] := With[{p = brt[n]}, {n, (n/2)^2, (n - p)*p, (n/2 - p)^2}] Your code for "area" uses an unnecessary loop variable (i) and three global variables. The latter point means the function has side-effects, as the values of m, k, and "hit" are changed in each call. Bobby On Wed, 6 Apr 2005 03:11:46 -0400 (EDT), Gilmar <gilmar.rodriguez at nwfwmd.state.fl.us> wrote: > Dear Mathematica User Group: > Without further a do; please download the following notebook to read my > two questions: > http://www.gilmarlily.netfirms.com/download/Questions.nb > (I'm using Mathematica version 5.1.1.0) > Your feedback is most welcome! Thank you! > > > > -- DrBob at bigfoot.com

**References**:**A question about a set-theory approach to minimal Goldbach prime partitions via Mathematica.***From:*"Gilmar" <gilmar.rodriguez@nwfwmd.state.fl.us>