Erdős's strong prime power conjecture for projective planes

A finite projective plane has an integer $n$, called its order, such that each line contains $n+1$ points, each point lies on $n+1$ lines, and there are $n^2+n+1$ points and lines. Projective planes of every prime-power order arise from finite fields, while it is not known whether other orders occur. Strong prime power conjecture. If a projective plane of order $n$ exists, then $n$ is a prime power. The existence of a projective plane of order $12$ is still unknown, and known results do not rule out projective planes for all sufficiently large multiples of $4$.