I've not seen a definition of "prime numbers" based on geometry and I wonder if there is one. It seems plausible that a definition is possible by using polygons or at least vertices/points and connections between them with some constraints.
Maybe something like;
For a set of [N > 2] points forming a polygon; N is prime if you cannot add internal non-overlapping edges resulting in all polygons with an equal number of vertices.
Of course, this doesn't cover 2 so it wouldn't be a general solution and may fail in other cases - I haven't put a lot of thought into it.
