[nycdatasci]

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-784801e4a6...

[mrabcx]

Tried the same prompt in DeepSeek 4

https://chat.deepseek.com/share/nyuz0vvy2unfbb97fv

Comes up with a proof.

[culi]

So 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

[adamgordonbell]

Are these proofs equivalent? Pretty cool if so.

[mrabcx]

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."