Singhi's conjecture on prime projective planes

A projective plane $\sigma$ is a subplane of a projective plane $\pi$ if $\sigma$ is a subsystem of $\pi$. A projective plane is prime if it has no proper projective subplane. Let $\mathcal{F}$ denote the free projective plane, and let projective planes over prime fields mean those over $\mathbb{Q}$ or over $\mathbb{F}_p$ for a prime $p$. Singhi's conjecture. The projective planes over prime fields and the free projective plane $\mathcal{F}$ are the only prime projective planes. Every prime projective plane is a homomorphic image of $\mathcal{F}$, which motivates the conjecture; its status is not resolved in the supplied text.