wow apparently there is now stronger result on large prime gap by GPT 5.6, improving beyond the previous best result of Ford-Green-Konyagin-Maynard-Tao [2014] by factor of log3 X / (log4 X)^2. I recall tao mentioning that it would require genuinely new idea to break his result, and that seems to be the case here.
+ its been verified in lean unconditionally?