This game is for any plural number of players.
Start with an n-by-n grid drawn on paper. (I suggest an n of at least 4 or 5 if there are two players who are beginners. I suggest a larger n if there are more players.)
The game starts with Player 1 placing any integer >=2 in any square of the grid.
Thereafter, the players take turns. On a turn a player places any integer >= 2 in any empty square that is adjacent to and above, below, left of, or right of any square with an integer in it already.
Each number must not have been used in the game yet.
And each number written down must be a divisor or a multiple of each preexisting number that is orthogonally (above, below, left of, right of) adjacent to it.
And each number written down must NOT be a divisor or a multiple of (may be coprime or not coprime to) each preexisting number that is diagonally adjacent to it.
The last player able to move wins.
Example finished game:
(n = 4. ** denotes an empty square. Leading 0's here are for formatting.)
** ** ** 15
** ** 10 05
08 04 02 **
** ** 06 03