Question: D.H.J. POLYMATH wrote in the paper Deterministic Methods To Find Primes the following statement:
"$\ldots$ the key observation is that the parity of the prime counting function $\pi(x)$ is closely connected to the divisor sum function, $\sum_{n \leq x}\tau(n)$."
I am asking for help in briefly describing the close connection. I was not able to follow the paper well enough to pick it up. Also am I correct in assuming parity in this context is referring to evenness and oddness of the number $\pi(x)$ ?