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We describe a rigorous algorithm to compute Riemann’s zeta function on the half line and its use to isolate the non-trivial zeros of zeta with imaginary part ≤ 30, 610, 046, 000 to an absolute precision of ±2−102. In the process, we provide an independent verification of the Riemann Hypothesis to this height.

Isolating some non-trivial zeros of zeta