Connections between prime numbers and geometry This might be a little open-ended, but I was wondering: are there any natural connections between geometry and the prime numbers? Put differently, are there any specific topics in either field which might entertain relatively close connections?
PS: feel free to interpret the term natural in a broad sense; I only included it to avoid answers along the lines of "take [fact about the primes] $\to$ [string of connections between various areas of mathematics] $\to$ [geometry!]"

Events on the horizon of a 2D Universe
You may have a look to the graph; it represents all the numbers (red, up to 100) that "see" straight to the origin.
e.g. prime 7 is represented by the seventh vertical point-column, prime 13 by the 13th column. The uniqueness of prime numbers is obvious.
