Problem 723

Erdős Problem #723 [status: falsifiable; formalized: yes]. If there is a finite projective plane of order $n$ then must $n$ be a prime power? A finite projective plane of order $n$ is a collection of subsets of $\{1,\ldots,n^2+n+1\}$ of size $n+1$ such that every pair of elements is contained in exactly one set. Current best: This conjecture has been proved for $n\leq 11$, but it is open whether there exists a projective plane of order $12$. Prize: no. Tags: combinatorics.