Developer's AI Engine Uncovers Systematic Error Pattern in Twin Prime Formula

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A software developer built an autonomous AI research engine called Luka and directed it toward the twin prime conjecture, one of mathematics' long-standing unsolved problems. Luka analyzed verified twin prime counts across 33 data points spanning eight orders of magnitude, from 10⁶ to 10¹⁴. It found that the residual between the widely used Hardy-Littlewood approximation and actual twin prime counts follows a consistent power law with an R² of 0.9907, later refined to 0.9997 with an additional logarithmic term. Further analysis revealed this pattern reflects a known second-order asymptotic error in the simplified approximation formula rather than a new property of twin primes themselves. Luka also tested and statistically falsified a recent oscillatory model called PRIT, whose predictions deviated from actual values by factors of 100 to 700.

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