  Hilberdink showed that there exists a constant $c_0>2$, such that there
exists a continuous prim system satisfying $N(x)=c(x-1)+1$ if and only if
$c\leq c_0$. Here we determine $c_0$ numerically to be $1.25479\cdot
10^{19}\pm2\cdot 10^{14}$. To do so we compute a representation for a twisted
exponential function as a sum over the roots of the Riemann zeta function. We
then give explicit bounds for the error obtained when restricting the occurring
sum to a finite number of zeros.
