On Tue, Jan 28, 2003 at 04:29:11PM -0000, jbrennen <

jack@...> wrote:

> --- Jon Perry wrote:

> It is easy to prove that k=9 is maximal, because you can't place

> 2,3,5,7, and 11 in a 4x4 square such that none of them touch.

Cool. And in general for an arbitrary prime Talisman Square the

maximum k will be p_M-p_m where m is the lowest prime index and

M = m + (floor((N+1)/2))^2

for an NxN matrix.

Using your example:

p_0=2

p_1=3

p_2=5

p_3=7

p_4=11

m=0

M=4

And for a 5x5 matrix starting at p_0, the maximal k is:

p_9 - p_0 = 29 - 2 = 27

This would work for a Talisman Square drawn from any ordered sequence.

Cheers,

Craig

--

Corollary to Clarke's Third Law:

Any technology distinguishable from magic is insufficiently

advanced.