I Pointed My AI Research Engine at Goldbach's Conjecture — It Found a Hidden Bias

Short summary

A developer built Luka, an AI research engine, and tested it against Goldbach's conjecture—discovering a previously unmeasured Chebyshev bias in partition counts across 2.5M integers. Statistical analysis (p = 4.07 × 10⁻²⁰⁴) reveals the Hardy–Littlewood formula systematically underpredicts representations for certain residue classes mod 3, a bias propagated through twin prime channels. The work demonstrates autonomous AI discovery in fundamental mathematics and includes reproducible code.

• •Developer built Luka AI engine to autonomously research Goldbach's conjecture
• •Discovered unmeasured Chebyshev bias in partition counts with p = 4.07 × 10⁻²⁰⁴
• •Demonstrates AI systems can make rigorous discoveries in fundamental mathematics

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