Applications of prime-number theorem in algebraic number theory? Dirichlet arithmetic progression theorem, or more generally, Chabotarev density theorem, has applications to algebraic number theory, especially in class-field theory.
Since we might think of the density theorem as an analytic theorem, and as prime number theorem is one main theorem of analytic number theory, one is led to wonder:  


if there is any application of prime number theorem to algebraic number theory.  


Thanks for any attention in advance.   

I don't know if this can be considered algebraic number theory or if it is more algebraic geometry; but, here goes.
Deligne uses the methods of Hadamard-de la Vallée-Poussin to prove the Weil conjectures. Even if it is not an application of the ordinary PNT as such, the exact same methods are applied elsewhere.
