Re: [PrimeNumbers] Re: Prime Talisman Squares
- On Tue, Jan 28, 2003 at 04:29:11PM -0000, jbrennen <jack@...> wrote:
> --- Jon Perry wrote:Cool. And in general for an arbitrary prime Talisman Square the
> 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.
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:
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.
Corollary to Clarke's Third Law:
Any technology distinguishable from magic is insufficiently