3 problems

Subbarao's conjecture. There are only finitely many unitary perfect numbers.

Let $H_{\mathrm{even}}$ be the set of even integers $m$ for which every prime divisor of $2^m+1$ is 3-Higgs. A prime is 3-Higgs when every prime divisor $q$ of $r-1$ satisfies…

The classification conjecture. The five integers above are the only unitary perfect numbers. No further unitary perfect number is known; this is the classical Subbarao–Warren probl…