![From https://www.erdosproblems.com/1196 :
PROVED (LEAN)
Is it true that, for any x, if A⊂[x,∞) is a primitive set of integers (so that no distinct elements of A divide each other) then
∑a∈A1aloga<1+o(1),
where the o(1) term →0 as x→∞?
#1196: [ESS68b][Er80,p.101]
number theory | primitive sets
A conjecture of Erdős, Sárközy, and Szemerédi. Lichtman [Li23] has proved that
∑a∈A1aloga<eγπ4+o(1)≈1.399+o(1).
This was solved by GPT-5.4 Pro (prompted by Price), which proved that for any primitive set A⊂N
∑a∈Aa>x1aloga≤1+O(1logx).
See the comment section for further refinements and discussion.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:fb5fjz7jxmbf3alhwh44ookd/bafkreihwwuqb3dmkhfghxntkjus2sjtphugn7nyc7a4bpliq4fk3bsqz64)
From https://www.erdosproblems.com/1196 : PROVED (LEAN) Is it true that, for any x, if A⊂[x,∞) is a primitive set of integers (so that no distinct elements of A divide each other) then ∑a∈A1aloga<1+o(1), where the o(1) term →0 as x→∞? #1196: [ESS68b][Er80,p.101] number theory | primitive sets A conjecture of Erdős, Sárközy, and Szemerédi. Lichtman [Li23] has proved that ∑a∈A1aloga<eγπ4+o(1)≈1.399+o(1). This was solved by GPT-5.4 Pro (prompted by Price), which proved that for any primitive set A⊂N ∑a∈Aa>x1aloga≤1+O(1logx). See the comment section for further refinements and discussion.
While AI attracts a lot of loud hype and haters, some mathematicians are happily using it to knock off unsolved problems. (I'm not saying anyone is "right" here.)
Recently Liam Price prompted GPT-5.4 Pro to prove this conjecture of Erdős:
chatgpt.com/share/69dd1c...
(1/n)
