An open problem in analytic number theory is to determine whether or not the following infinite series converges:

$\sum_{n=2}^{\infty} \frac {(-1)^{\pi(n)}}{n log n}$

Here, $\pi(n)$ is the prime counting function so the problem reduces to understanding the parity of this function. I suspect that the sum converges after some numerical calculations but I don't know what type of theorem needs to be established to prove convergence. I posted the problem on Terry Tao's blog and he tells me that some kind of equidistribution theorem is needed but I don't have any idea how to even formulate it. Does any one have any ideas?