Riemann Hypothesis

Hypothesis
All the nontrivial zeroes of the analytic continuation of the Riemann zeta function have a real part equal to $$\frac 1 2$$.

Trivial zeroes occur at every negative even integer ($$-2, -4, -6$$ etc.)

Comment
This problem is no 8 in the Hilbert 23, and also one of the Millennium Problems, the only one to be in both lists.