GPT-5.4 Pro solves Erdős Problem #1196

> Appreciate the insight! If it's at all of interest, this was a one-shot (supposed) solution in about 80 mins, unlike some other problems like 851 that took over 20 continuations totalling perhaps 15-20 hours of reasoning time.

Source: https://www.erdosproblems.com/forum/thread/1196#post-5365

> I care deeply about this problem, and I've been thinking about it for the past 7 years. I'd frequently talk to Maynard about it in our meetings, and consulted over the years with several experts (Granville, Pomerance, Sound, Fox...) and others at Oxford and Stanford. This problem was not a question of low-visibility per-se. Rather, it seems like a proof which becomes strikingly compact post-hoc, but the construction is quite special among many similar variations.

> The conjecture is 60 years old and many experts had consulted on the problem, making partial progress. I mentioned this to @thomasfbloom, and he replied: "perhaps the first Book Proof from AI?"

Terence Tao says:

> In any case, I would indeed say that this is a situation in which the AI-generated paper inadvertently highlighted a tighter connection between two areas of mathematics (in this case, the anatomy of integers and the theory of Markov processes) than had previously been made explicit in the literature (though there were hints and precursors scattered therein which one can see in retrospect). That would be a meaningful contribution to the anatomy of integers that goes well beyond the solution of this particular Erdos problem.