David Platt and Timothy Trudgian used rigorous interval arithmetic to verify that all zeros of the Riemann zeta function with imaginary part up to 3x10^12 lie on the critical line and are simple, published in the Bulletin of the London Mathematical Society in 2021. Earlier non-rigorous computations covered more zeros, but this is the largest rigorously certified range.
The question, scope, and sources behind this Registry record.
David Platt and Timothy Trudgian used rigorous interval arithmetic to verify that all zeros of the Riemann zeta function with imaginary part up to 3x10^12 lie on the critical line and are simple, published in the Bulletin of the London Mathematical Society in 2021. Earlier non-rigorous computations covered more zeros, but this is the largest rigorously certified range.
The largest T such that every nontrivial zero of the Riemann zeta function with 0 < Im(s) ≤ T is rigorously proven to have real part 1/2.
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Current frontiers derived from accepted Claims.
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The frontier as it changed over time.
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1 accepted Claim, with 1 linked evidence records.
Permanent ID limitsregistry.com/limits/LR-RIEMANN-HYPOTHESIS-VERIFICATION-HEIGHT
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Limits Registry. LR-RIEMANN-HYPOTHESIS-VERIFICATION-HEIGHT. Largest height to which the Riemann hypothesis has been rigorously verified. 2026.