  Let $\mathcal L^+$ be the set of all primes $p$ for which the sums of
$\left(\frac{n}{p}\right)$ over the interval $[1,N]$ are non-negative for all
$N$. We prove that the estimate \[ |\mathcal L^+\cap [1,x]|\ll \frac{x}{\ln
x(\ln\ln x)^{c-o(1)}} \] holds for $c\approx 0.0368$
