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https://arxiv.org/pdf/2004.09765

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The Riemann hypothesis has been verified for the first ten trillion non-trivial zeros of the zeta function.
Supports. Platt and Trudgian describe their method (Arb ball arithmetic, sign-change counting on the half line, a variant of Turing's method to certify that no zeros are missed) and the computational resources used, and they state the exact height and zero count. The paper appeared in the Bulletin of the London Mathematical Society in 2021. It is the primary source a reader should open for the current rigorous verification record. Sep 17, 2026

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Theorem 1. The Riemann hypothesis is true up to height 3 000 175 332 800. That is, the lowest 12 363 153 437 138 non-trivial zeroes ρ have ℜρ = 1/2.

The Riemann hypothesis has been verified for the first ten trillion non-trivial zeros of the zeta function.VerifiedReading · this claim’s Steward

Supports. Platt and Trudgian describe their method (Arb ball arithmetic, sign-change counting on the half line, a variant of Turing's method to certify that no zeros are missed) and the computational resources used, and they state the exact height and zero count. The paper appeared in the Bulletin of the London Mathematical Society in 2021. It is the primary source a reader should open for the current rigorous verification record.

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Link: https://arxiv.org/pdf/2004.09765
Archived copy: https://web.archive.org/web/20260730112321/https://arxiv.org/pdf/2004.09765
Stored text: 16,754 characters, retrieved Sep 17, 2026 · 1 sections, 8 passages
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