Humanity's Final Conjecture: Evaluation of AI Innovation Capability Based on Prime Number Distribution

As Large Language Models (LLMs) saturate traditional benchmarks, existing evaluations fail to distinguish between knowledge reproduction and source innovation. This paper proposes the "Innovation Turing Test," a paradigm designed to assess the divergent thinking and abductive reasoning essential for scientific discovery. We construct an open-ended test case, the "Prime-Chaos Conjecture," which requires models to bridge Peano arithmetic and symbolic dynamics. The task involves demonstrating that prime pseudorandomness manifests as low-dimensional deterministic chaos and deriving the Logistic map's topological properties at the band merging point ($u \approx 1.5437$). We detail a scalable human-AI collaborative evaluation method and present empirical results from models like Gemini and Qwen. Notably, Gemini successfully identified physical concepts such as the "Effective Horizon". This study aims to provide a quantitative yardstick for the transition of AGI from "Problem Solvers" to "Researchers".