Comment by nycdatasci
12 hours ago
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...
Tried the same prompt in DeepSeek 4
https://chat.deepseek.com/share/nyuz0vvy2unfbb97fv
Comes up with a proof.
Are these proofs equivalent? Pretty cool if so.
No, 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."