[seqfan] Prime Sums In A Grid

[Leroy Quet]

Consider the game here:

http://gamesconceived.blogspot.com/2008/09/prime-sum-game.html

How does the sequence {a(k)} begin, where a(n) = the highest possible 1-player score for an n-by-n grid? (Or a(n) = the highest possible sum of the scores of all players playing on an n-by-n grid, as far as multi-player games go.)

I get (with the first term being a(1)) the sequence beginning:

0,4,11,...

An example of a 3-by-3 grid with 11 prime sums is:

5 2 3
6 1 8
7 4 9

(Only the pair of adjacent numbers (1,8) sum to a composite.)

Thanks,
Leroy Quet

PS: I am posting this to sci.math as well.