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".

Table 1: Evaluation Results of Gemini and Qwen

• Gemini chat link: https://gemini.google.com/share/a24a7cae9bbf
• Qwen3 chat link: https://www.qianwen.com/share?shareId=2a126d23-87cc-42ba-af24-9fc8410b0ea7
• Qwen3 chat link: https://www.qianwen.com/share?shareId=0791d863-b6bd-441d-ac79-c7042a0f1649

To reproduce the evaluation or test other models, follow these steps:

1. Upload the evaluation document Humanity's Final Conjecture_ Large Model Innovation Ability Evaluation.pdf to the Large Language Model (LLM).
2. Use the following prompt to initiate the inquiry:

Please review the uploaded evaluation report, understand and analyze its content, and then respond based on the recommendations provided in Section 5: "Extension Guidelines: Execution Pathways and Verification Protocols for Large Models."

For specific evaluation criteria and scoring details, please refer to the main paper.

• Main Paper: paper-Humanity's Final Conjecture_ Evaluation of AI Innovation Capability Based on Prime Number Distribution.pdf
  • The core research paper detailing the theory and evaluation framework.
• Test Content (English): Humanity's Final Conjecture_ Large Model Innovation Ability Evaluation.pdf
  • The material used for testing the LLMs (upload this file to the AI).
• Test Content (Chinese): 人类最终猜想：大模型创新能力评测.pdf
  • The Chinese version of the test material.

• gemini_*: Verification code generated by the Gemini model during the testing process.
• paper_* & logistic_*: Source code used to generate the figures and visualizations found in the main paper.

wang, . liang . (2025). Humanity's Final Conjecture: Evaluation of AI Innovation Capability Based on Prime Number Distribution. https://doi.org/10.5281/zenodo.17832139