alt Hacker NewsJust two days ago, a preprint by Julia Stadlmann went up on arXiv [0] improving the prime gap from 246 to 240. Now OpenAI announces Astra has shown a gap of 186 [1]. That must really blow.
[0] https://arxiv.org/abs/2608.31126
[1] https://cdn.openai.com/pdf/51126fac-1b68-4128-9666-c908bcc16...
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I think this builds straight upon her method, which she said could be improved herself so...
With very little review: https://github.com/openai/PrimeGaps186/blob/main/formalizati...
"No independent human semantic review. Whole-file sorry counts and a complete auxiliary-declaration audit are not established; separate declaration lint has not been run."
Don't think everything is just "who can produce the biggest/smallest number": https://mathstodon.xyz/@tao/117208619314517025.
What's just as interesting is this morning Axiom Math announced 212 and OpenAI then appears to have rushed out their 186 announcement just 1-2 hours later followed by Astra. Did they accelerate the release of Astra itself? Not necessarily, but it definitely looks like they ended up pushing much harder and faster than planned on their 186 result. X activity suggests Anthropic had a similar result as well but wasn't as fast as OpenAI in packaging it up and sharing it in response to Axiom, so they mostly just bolted onto OpenAI's messaging.
The reason I think this is interesting is that Axiom is a tiny lab in comparison that wouldn't have had access to Astra at all. I'd be curious to learn how Axiom is able to effectively compete at this frontier with vastly fewer resources.
Ok, so the rumour was exactly true: there was a withheld prime gaps improvement, that "an AI company" was holding onto until release of a model.
Where did you get the link to the pdf? Was it announced somewhere?
Happened to multiple people I know.
Such a result should be considered worthless: the proof is 10MB of Lean. (https://github.com/openai/PrimeGaps186).
I can't think of a single mathematical proof being anywhere close to ten million characters. For all you know, 90% of the proof could be useless, 8% would be writing out Shakespeare, and 1% abusing another bug in Lean. Humanity gets zero value from that, aside from "some bot seems to think it's 186". Unusable by anyone.
Based on her comments in the paper it sounds like she was aware that an AI result was coming and rushed to release her work beforehand. 240 was not a tight bound from her methods.