What would be the best lower bound for the number of squares modulo p$p$ in an interval [1,N]$[1,N]$ with N<p$N<p$ that are prime?
Via the Burgess bound, I can find a lower bound for the number of squares modulo p$p$ in [1,N]$[1,N]$, but I would need a bound for the number of squares that are also prime. Since the size of N$N$ matters, in my particular case I have N=sqrt(p)/2.
$$
N=\frac{\sqrt{p}}{2}.
$$
Thank you very much!