  We prove a highly uniform version of the prime number theorem for a certain
class of $L$-functions. The range of $x$ depends polynomially on the analytic
conductor, and the error term is expressed in terms of an optimization problem
depending explicitly on the available zero-free region. The class contains the
Rankin-Selberg $L$-function $L(s,\pi \times \pi')$ associated to cuspidal
automorphic representations $\pi$ and $\pi'$ of $\mathrm{GL}_{m}$ and
$\mathrm{GL}_{m'}$, respectively. Our main result implies the first uniform
prime number theorems for such $L$-functions (with analytic conductor
uniformity) in complete generality.
