Squares Overlapping/ Subdividing Into Primes

Here is a game for any number of players.

Play a number of rounds, where the number of rounds is a multiple of the number of players. Each player plays the same number of rounds as offense.

Start each round with with an n-by-n grid lightly drawn on paper, where n is at least 15 or more and is finite. (And n is the same value for all rounds.)


On a round the players take turns boldly drawing the perimeters of squares along the lines of the grid. The edges of the squares may overlap. But each player must darken in at least some segment(s) of grid-lines that have not yet been part of any edge of any previously drawn square.

After a predetermined number of moves (the same number for all rounds), then the offense player tries to find the largest CONTIGUOUS collection of regions bordered by the bold lines that have a total of a prime number of grid-squares in them.
(The regions can be of any shape, and may be made by adding squares together or by taking smaller squares out of larger regions, for example.)

The offense player gets this prime added to their score.

After all rounds are played, the player with the highest total score wins.

Thanks,
Leroy Quet