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