I have an idea on how this could be generalized.
The first prime after 97, 101, has the effect of "play two 1 stones off of this stone": the first 1 must be played adjacent to the 101, the second must be adjacent to either the 101 or the first 1. (Or, if that's too complicated, 101's effect can just be "add two 1 stones to your hand"). 103 plays/adds two 2 stones, 107 plays/adds two 3 stones, 109 plays/adds two 4 stones, and so on.