  The main goal of this note is to establish the limits of L. Zhao's techniques
for counting solutions to quadratic forms in prime variables. Zhao considered
forms with rank at least 9, and showed that these equations have solutions in
primes provided there are no local obstructions. We consider in detail the
degenerate cases of off-diagonal rank 1 and 2, and improve the rank lower
bounds to at least 6 and at least 8 respectively. These results complement a
recent breakthrough of Green on the non-degenerate rank 8 case.
