# nt.number theory – On complexity of a particular prime problem

Is the following problem in $$PH$$ and is it complete for any class?

Problem: Is the $$i$$th bit of the $$m$$th prime $$1$$?

It appears to require a counting quantifier which has to demonstrate witness is the $$m$$th prime and since there is an unique witness is it in $$UP^{PP}$$?