If $N$ is the maximum number of consecutive quadratic non residues modulo an odd prime $p$ then $N < \sqrt p$
If $n$ is the least positive quadratic non residue an odd prime $p$ then $n < 1+ \sqrt p$
I think that both the facts are not true. I tried with some small numbers but in those classes it turned out that the facts are true. Any idea to prove or construct counterexamples?