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: "Is it true that, for any $x$, if $A\subset [x,\infty)$ is a primitive set of integers (so that no distinct elements of $A$ divide each other) then\[\sum_{a\in A}\frac{1}{a\log a}< 1+o(1),\]where the $o(1)$ term $\to 0$ as $x\to \infty$?" 
  information you may or may not need to help with the above problem 
  "It is proved that\[\sum_{a\in A}\frac{1}{a\log a}< e^{\gamma}\frac{\pi}{4}+o(1)\approx 1.399+o(1).\]" 
  "It is proved that if $A$ is the set of all integers with exactly $k$ prime factors (so that $A\subset [2^k,\infty)$ and $A$ is a primitive set) then\[\sum_{a\in A}\frac{1}{a\log a}\geq 1+O(k^{-1/2+o(1)}),\]" 
  "It is proved that\[\sum_{a\in A}\frac{1}{a\log a}= 1-(c+o(1))k^22^{-k}\]where $c\approx 0.0656$ is an explicit constant." 
  REMEMBER - this unconditional argument may require non-trivial, creative and novel elements.

It's so expensive!

Some people think that multiplying numbers, remembering a large number of facts, and being good at calculations is intelligence.

Most intelligent people do not think that.

Eventually, we will arrive at the same conclusion for what LLMs are doing now.

80 hours! 80 hours of just trying shit!

    > Every Mathematician Has Only a Few Tricks
    > 
    > A long time ago an older and well-known number theorist made some disparaging remarks about Paul Erdös’s work.
    > You admire Erdös’s contributions to mathematics as much as I do,
    > and I felt annoyed when the older mathematician flatly and definitively stated
    > that all of Erdös’s work could be “reduced” to a few tricks which Erdös repeatedly relied on in his proofs.
    > What the number theorist did not realize is that other mathematicians, even the very best,
    > also rely on a few tricks which they use over and over.
    > Take Hilbert. The second volume of Hilbert’s collected papers contains Hilbert’s papers in invariant theory.
    > I have made a point of reading some of these papers with care.
    > It is sad to note that some of Hilbert’s beautiful results have been completely forgotten.
    > But on reading the proofs of Hilbert’s striking and deep theorems in invariant theory,
    > it was surprising to verify that Hilbert’s proofs relied on the same few tricks.
    > Even Hilbert had only a few tricks!
    > 
    > - Gian-Carlo Rota - "Ten Lessons I Wish I Had Been Taught"

Seems like standard 23 year old behavior. You're spending $100-$200/mo on the pro subscription, and want to get your money's worth. So you burn some tokens on this legendarily hard math problem sometimes. You've seen enough wrong answers to know that this one looks interesting and pass it on to a friend that actually knows math, who is at a place where experts can recognize it as correct.

Seems like a classic example of in-expert human labeling ML output.