Anthropic's Claude AI makes mathematical breakthrough in prime number research

Anthropic’s AI model, Claude, has achieved a new mathematical result related to the distribution of prime numbers while attempting to solve the 170-year-old Riemann Hypothesis. Although the model did not prove the hypothesis itself, it established a new lower bound for the percentage of non-trivial zeros of the Riemann zeta function that lie on the critical line.

Specifically, the research version of Claude demonstrated that at least 67.2% of these zeros are on the critical line, a significant increase from the previous minimum threshold of 41.6%. This finding represents progress in a related mathematical problem rather than a complete solution to the hypothesis.

The research process involved Claude testing 650 unsuccessful ideas and utilizing 60 agentic instances to verify different approaches. Human researchers provided minimal mathematical guidance, focusing instead on encouraging the model during the autonomous research process.