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!]"

Well, prime numbers are strongly related to the Riemann zeta function, $\zeta(s)$. This has a product representation which involves the roots of the function. The Riemann Hypothesis now states that all non-trivial roots in the complex plane lie on the "critical line":
$$Re(z)=\frac12$$
which can be thought of as a geometric feature.
