  Let E_x(q,a) be the error term when counting primes in arithmetic
progressions and let M(Q)=sum_{q<Q}phi(q)\sum_{a=1}^qE_x(q,a)^3. We show that
M(Q)<<Q^3(x/Q)^{4/3} for large Q close to x (in the usual BDH sense) thereby
showing that sign changes in the error give power saving cancellation past the
expected root(x/q) heuristic.
