Recommend a good read on prime sieving, which can be applied to sieve primes of the form $x^2 + y^2$ (or $x^2 + ny^2$, if possible).
I actually need to find up to a certain limit numbers that are simultaneously representable as $x^2+y^2$ and $x^2+2y^2$ and $x^2+3y^2$. I know which primes can be representable in these forms, and then Eratosthenes sieve can be applied... But I thought there might be something more efficient.
Thank you!