SITUATION EXPLAINED: Claude raised the Riemann hypothesis lower bound from 41.6% to 67.2%. • It was asked to take a real stab at the Riemann hypothesis itself. It didn't solve that, but improved a related bound along the way • The bound is the fraction of zeros of the Riemann zeta function proven to satisfy the hypothesis • The prompt came from Jarred Sumner, creator of Bun and a non-mathematician • Its first attempt tried 650 ideas and failed. On the second, Claude spent a day and a half…

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We asked an unreleased research version of Claude to take a stab at the Riemann hypothesis. It didn’t solve it, but it did make strides on a related problem: it increased the lower bound for the fraction of zeros of the Riemann zeta function that satisfy the hypothesis from 41.6% to 67.2%. https://www.anthropic.com/research/riemann-zeta