TITLE: If $m,n$ are relatively prime, are there an infinitude of primes $mx^2 +n$
QUESTION [5 upvotes]: I know that Dirichlet's theorem says that there are an infinite number of primes of the form $mx+n$
I was wondering what we know when $x$ is squared.
If for any reason we don't know if there are infinite primes, can we say anything about the number of semiprimes of this form?
Thanks,
-Larry

REPLY [3 votes]: Alright, Iwaniec has shown that infinitely many $x^2 + 1$ are either prime or semiprime. Maybe other polynomials as well.  https://oeis.org/A248742