Uniform distribution conjecture for prime values of a polynomial

Let $f(x)\in\mathbb{Z}[x]$ produce infinitely many primes. A congruence class modulo a positive integer $m$ is $m$-allowable for $f(x)$ if $(f(r),m)=1$ for every integer $r$ in that class. Uniform distribution conjecture. For every positive integer $m$, the integers $n$ for which $f(n)$ is prime are asymptotically uniformly distributed over the $m$-allowable congruence classes for $f(x)$. Equivalently, if $A_m(f)$ is the number of such classes, each allowable class has limiting relative frequency $1/A_m(f)$. This conjecture is presented as an important distributional hypothesis in the paper and is not known in general.