conjecture: if p is prime, the no. of rings of order p^2 is 11

[Richard Mathar]

>  "This completes the discussion and we see that there are in
>  all 3+2+2+3+1=11 mutually nonisomorphic rings of order p^2"
>
>  on page 228 of
>  R. Raghavendran, Finite associative rings,
>  in: Compositio Mathematica, vol 21, no 2 (1969) p195-229,

Nice find !
Directly after that phrase, he also gives the number of nonisomorphic
rings of order p^3:

    THEOREM 14. The exact number of mutually nonisomorphic rings
of order p^3, each possessing an identity element, is eleven or twelve
according as the prime p is even or odd. Only one of these rings is
noncommutative - (...).

So this is "almost" a function of the prime signature (i.e. the same
for all odd prime cubes).

Maximilian