There's a standard question I ask to test llms: to produce an Agda proof that there are infinitely many prime numbers. None of them have succeeded. Here is the result for DeepSeek's R1 model. R1 is a "chain of thought" model, on par with OpenAI's o1. However, unlike OpenAI, DeekSeek makes the chain of thought publicly available, giving us some insight on the process it follows to get the answer.
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