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Aug 24, 2017 at 23:40 vote accept Milin
Aug 24, 2017 at 15:52 comment added user41593 I should add that this is comparatively much harder than Mills's theorem, just as Mills's relies on much deeper results than for Wright's constant (spacing between successive primes vs. Bertrand's postulate); an argument for not expecting such an $\alpha$ is that if you run an analogous argument you need an estimate on primes which is too good to be true.
Aug 24, 2017 at 15:30 history answered user41593 CC BY-SA 3.0