AI Research Engine Detects Unmeasured Chebyshev Bias in Goldbach's Conjecture

A developer built an autonomous AI research tool called Luka and directed it at Goldbach's conjecture, one of mathematics' oldest unsolved problems. Luka computed Goldbach partition counts for over 2.4 million even integers and found that numbers in residue class n ≡ 1 (mod 3) have approximately 0.26% more Goldbach representations than those in n ≡ 2 (mod 3), contradicting the Hardy–Littlewood formula's prediction of symmetry between the two classes. Statistical tests returned an extraordinarily low p-value of 4.07 × 10⁻²⁰⁴, making the result highly unlikely to be random noise. The developer attributes the bias to Chebyshev's known tendency to favor primes of certain residue classes, an effect that gets amplified through the bilinear structure of Goldbach partition counts. The project, built using Python and open-sourced on GitHub, is presented as a proof of concept for AI-assisted autonomous mathematical discovery.