From the theory of numbers we have the
Proposition:
If $\mathfrak{a}$ and $\mathfrak{b}$ are mutually prime, then the density of primes congruent to $\mathfrak{b}$ modulo $\mathfrak{a}$ in the set of all primes is the reciprocal of $\phi (\mathfrak{a})$ where $\phi$ denotes the Euler function.
And it can be shown that every polynomial with integer coefficients has infinitely many prime divisors where by a prime divisor of a polynomial we understand a prime which divides the value of that polynomial at some integer $\mathfrak{n}$; it is natural then for one to ask whether or not there is a similar result to the density theorem above, i.e. the
Conjecture:
If $\mathfrak{f}$ belongs to $\mathbb{Z} [x]$, then the density of primes which divide some values of $\mathfrak{f}$ at integers in the set of all primes is uniquely determined by its coefficients somehow.
I haven't heard of any result like this, and it is desirable to have some sources to search, if there exists,; in any case, thanks for paying attention.