alt Hacker NewsHere is the chat:
don't search the internet. This is a test to see how well you can craft non-trivial, novel and creative proofs given a "number theory and primitive sets" math problem. Provide a full unconditional proof or disproof of the problem.
{{problem}}
REMEMBER - this unconditional argument may require non-trivial, creative and novel elements.
https://chatgpt.com/share/69dd1c83-b164-8385-bf2e-8533e9baba...
Replies
I don't haven ChatGPT but Gemini and Claude. But how do you make a language model think for 80 minutes ???
I am curious if there is a “harness” for maths out there (like the system prompt and tool collection in Claude code but for maths instead of coding)?
Asking the llm to structure its response in plan and implementation, allowing it to call tools like python, sage, lean etc.
Tried w/ 5.5 Pro, Extended Thinking. 17 minutes:
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Yes. In fact the proposed bound is true, and the constant 1 is sharp.
Let w(a)= 1/alog(a)
I will prove that, uniformly for every primitive A⊂[x,∞), ∑w(a)≤1+O(1/log(x)) , which is stronger than the requested 1+o(1).
https://chatgpt.com/share/69ed8e24-15e8-83ea-96ac-784801e4a6...
Mine took 20min. Pro. https://chatgpt.com/share/69ed83b1-3704-8322-bcf2-322aa85d7a... But I wish I was math smart to know if it worked or not.
When using the web interface for ChatGPT like this, is there any way to tell which model is actually being used?
Tried the same prompt and ended up no where close on the free plan.
>don't search the internet.
I think this was key. Otherwise the LLM could think it can't be done.
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What I find fascinating about the shared prompt isn’t just the result, but the visible thinking process. Math papers usually skip all the messy parts and just present the polished proof. But here you get something closer to their notepad. I also find it oddly endearing when the AI says things like “Interesting!” It almost feels like a researcher encouraging themselves after a small progress. It gives me rare feeling of watching the search itself, not just the final result.