The 10 sup (20th) zero of the Riemann zeta function and 70 million of its neighbors.

This paper presents the results of a computation of almost 79 million consecutive zeros of the Riemann zeta function near zero number 10 sup 20, as well as several other large sets of high zeros. These zeros lie about 10 sup 8 times higher than previously calculated large sets of zeros, and their computation was made possible by a fast new algorithm invented by A. Schonhage and the author. Although the implementation of this algorithm that was used is not entirely rigorous due to incomplete control of roundoff errors, it appears to be highly accurate as well as fast, and the results indicate that all the computed zeros satisfy the Riemann Hypothesis.