Developer's AI Engine Finds Power Law Pattern in Twin Prime Approximation Error

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A software developer built an autonomous AI research engine called Luka and directed it at the twin prime conjecture, one of mathematics' long-standing unsolved problems. Luka analyzed 33 verified twin prime data points spanning 10⁶ to 10¹⁴ and found that the residual error in the widely used Hardy-Littlewood approximation follows a consistent power law with R² of 0.9907. Further analysis revealed this pattern stems from a known second-order term in the asymptotic expansion of the logarithmic integral, rather than a novel property of twin primes themselves. Luka also tested a recent oscillatory model called PRIT against 200 high-precision Riemann zeta zeros, finding its predictions were off by factors of 100 to 700, effectively falsifying it. The developer has published the findings and code on GitHub, framing Luka as a proof-of-concept for AI-driven autonomous mathematical research.

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