       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>
• 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:
> two questions:
> (I'm using Mathematica version 5.1.1.0)
> Your feedback is most welcome! Thank you!
>
>
>
>

--
DrBob at bigfoot.com

```

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