  We show under the Generalised Riemann Hypothesis that for every $\delta>0$,
almost every prime $q$ in $[Q,2Q]$ has the expected of prime primitive roots in
the interval $[x,x+x^{\frac{1}2+\delta}]$ provided $Q$ is not more than
$x^{\frac{2}{3}-\epsilon}$. We obtain this via a variant of the classical
truncated Perron's formula for the partial sums of the coefficients of a
Dirichlet series.
