# Re: Prime Sums In A Grid

*From*: LudovicoVan <julio@xxxxxxxxxxxxx>*Date*: Tue, 24 Feb 2009 23:31:46 -0800 (PST)

On 24 Feb, 22:32, bart demoen <b...@xxxxxxxxxxxxxx> wrote:

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

Hello Bart,

Thank you too very much for the feedback.

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.

Right, I had been thinking about that, but couldn't come up with any

clever way to avoid symmetric solutions. A simple approach I could

think of was: take three distinct numbers (say, 1, 2 and 3), and

impose the contraint that they appear in a specific left-right/up-down

orientation, but that's not enough because some solutions might have

the three numbers lined up in a row, so something more clever is

needed. I'll keep thinking about this problem, but, as I was

anticipating to Markus, not until tomorrow (or maybe even later

tonight, if I am not too destroyed by the working day).

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 ?

No, no proof so far from the guys in sci.math, and surely not from

myself. That's why I was after some more evidence. Very interesting

that you seem not to find any solution for some values of N, as my

guess was the number of solutions could only increase for increasing

values of N.

-LV

.

**References**:**Re: Prime Sums In A Grid***From:*Markus Triska

**Re: Prime Sums In A Grid***From:*LudovicoVan

**Re: Prime Sums In A Grid***From:*bart demoen

- Prev by Date:
**Re: Prime Sums In A Grid** - Next by Date:
**Re: Prime Sums In A Grid** - Previous by thread:
**Re: Prime Sums In A Grid** - Next by thread:
**Re: Prime Sums In A Grid** - Index(es):