3 ms·
Tried w/ 5.5 Pro, Extended Thinking. 17 minutes: ----------------------------- Yes. In fact the proposed bound is true, and the constant 1 is sharp. Let w(a
by nycdatasci 6mo ago
Tried w/ 5.5 Pro, Extended Thinking. 17 minutes:
-----------------------------
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-784801e4a6ec https://chatgpt.com/share/69ed8e24-15e8-83ea-96ac-784801e4a6...
- mrabcx 6mo agoTried the same prompt in DeepSeek 4 https://chat.deepseek.com/share/nyuz0vvy2unfbb97fv https://chat.deepseek.com/share/nyuz0vvy2unfbb97fv Comes up with a proof.
- adamgordonbell 6mo agoAre these proofs equivalent? Pretty cool if so.
- mrabcx 6mo agoNo, they do not seem to he equivalent. Not a mathmatician but running the Deepseek proof through ChatGPT gives: "If everything is made rigorous: You would have a valid independent proof It would contain real structural insight It would not replace the flow proof as the “best” proof But: It would still be a meaningful alternative proof with explanatory power, not just a redundant one."
- culi 6mo agoSo DeepSeek, GPT, and presumably many other LLMs are capable of solving this problem and even producing independent unique proofs. I wonder if this particular Erdos problem is unique in that solvability