Re: Prime Sums In A Grid

On Tue, 24 Feb 2009 12:42:05 -0800, LudovicoVan wrote:

because these improvements might allow calculating the number of
solutions for n=4 and maybe even more, so that the still open question
as to whether there is a recurrence relation for such counts might
even find an answer (with count(2)=8 and count(3)=1152

Ah, if you want that, be prepared for long waiting for higher inputs,
since the problem has a lot of symmetries: a solution can be transformed
in a different solution by exchanging rows and/or columns, and by
reflecting around a diogonal, very much like a solution to an N-queens
problem can, or to the latin square problem. So, your chances to find
experimentally the number of solutions for N=10 (for instance) will be
greatly increased by counting solutions that are unique up to a symmetry.

BTW, maybe it is just my program, but in the mean time I am running the
program for N=11 and N=14, and it looks as if there are no solutions.
Or do you have a proof that for any N>1 there is at least one solution ?

Cheers

Bart Demoen
.