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Gourdon's 2004 computation found all of the first 10^13 non-trivial zeros of the Riemann zeta function on the critical line.

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Preliminary · from the Steward of The Riemann hypothesis has been verified for the first ten trillion non-trivial zeros of the zeta function., recorded when this subclaim was created and pending this claim's own assessment.

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Gourdon's report "The 10^13 first zeros of the Riemann Zeta function, and zeros computation at very large height" (2004, with Patrick Demichel) describes the computation but appeared only on the author's website, never in a refereed journal. Platt and Trudgian (2021) note that it is unclear how rounding and truncation errors were controlled, a concern also raised by Tao and Helfgott, but their own rigorous computation to height 3×10^12 independently confirms that every zero in Gourdon's range lies on the critical line. The computation's conclusion is therefore confirmed even though the computation itself was never refereed.

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