AI Research Engine Detects Unmeasured Chebyshev Bias in Goldbach Partition Counts

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 congruent to 1 (mod 3) consistently produce 0.26% more prime-pair representations than those congruent to 2 (mod 3). This asymmetry contradicts the Hardy–Littlewood formula, which predicts equal counts for both residue classes, and was confirmed with an exceptionally low p-value of 4.07 × 10⁻²⁰⁴. The developer attributes the bias to Chebyshev's known tendency to favor primes in certain residue classes, a effect that appears to amplify when convolved through Goldbach's bilinear structure. The findings, shared on DEV Community along with open-source Python code, are presented as a proof of concept for AI-assisted mathematical discovery rather than a formal peer-reviewed proof.