I am interested in the following problem:
Let $n$ be a fixed positive integer. What is the approximate number of primes $n \leq p \leq n^2+n$ such that $p-n$ is a perfect square.
It is not difficult to approximate the total number of primes in the interval $[n,n^2+n]$, for example by using the prime number theorem. However, I don't know how to locate this specific set of primes.
I assume that some sort of sieve argument might be helpful, but I do not have much experience with that, so any suggestions in this direction are very welcome.
Thanks!