I'm interested in calculating all of the zeroes of the first derivative of the Riemann $\zeta$ function. I know that (on the RH), all of these zeroes will have real part $\geq \frac{1}{2}$. I am curious if there are equally strong upper bounds.
According to Titchmarsh, there is a constant $c$ ($2<c<3$) such that every zero of $\zeta$'(s) has real part less than c. Skorokhodov showed that $c<2.93938$.
Does anyone know what the sharpest upper bound on c is?