Building on its broad strengths in mathematics in general, and in special functions in particular, Mathematica provides a unique level of support for analytic number theory, including not only highly general function evaluation, but also symbolic simplification.
Zeta — Riemann zeta function
PrimeZetaP — prime zeta function
DirichletL — Dirichlet L-function
PrimePi — prime counting function
Prime — the n prime number