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Notes -
In the announcement blog post, footnotes 9 and 10 concern mathematical discoveries regarding prime gaps. In 9 they link to proof to there being an infinitely many primes that differ by at most 186, in 10 that there are infinitely many primes p_n that are greater than the previous prime p_(n-1) by at least ln(n)ln(ln(n))^2 ln(ln(ln(ln(n))))/ln(ln(ln(n)))^2.
Not linked in the announcement, but also products of this model are: disproof of Erdos Problem 1 (according to Bloom's numbering), disproof of EP74, proof of EP126, proof of EP548, proof of EP571.
As mathematician's are usually asked to pre-review OpenAi's proofs (but not those published by Alpöge of Anthropic), Terence Tao must have known about this prior to thus publication. This would explain today's doomposting of his on mathstodon about how open problem are needed by mathematician to discover new techniques and proposing certain problems be offlimits to AI investigation. In my mind this summoned a thought of ChatGPT treating a prompt to consider prime gaps as it does a prompt about explossive manufacture.
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