Recall $\pi(n)$ the number of primes $\le n$ is the prime-counting function. By "PRIMES in P", computing $\pi(n)$ is in #P. Is the problem #P-complete? Or, perhaps, there is a complexity reason to believe that this problem is not #P-complete?
P.S. I realize this is a bit naive since somebody must have studied the problem and proved/disproved/conjectured this, but I can't seem to find the answer in the literature. See here if you are curious why I care.