[seqfan] Re: Maximal prime gaps

[Trizen]

Just an observation:

Limit_{p -> Infinity} (p^(p^(1/p)) - p - log(p)^2) = 0

Therefore, if a counter-example exists, it should be just as hard to find
as finding a counter-example to Cramer's conjecture.

On Mon, Feb 20, 2023 at 11:36 AM Tomasz Ordowski <tomaszordowski at gmail.com>
wrote:

> Hello!
>
> Conjecture:
> if p > 3, then q < p^(p^(1/p)),
> where q is the next prime after p.
>
>   Is there a counterexample?
>
> Similar to Firoozbakht's conjecture,
> this is close to Cramer's conjecture:
> q - p = O(log p)^2.
>
> Best,
>
> Thomas
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> https://en.wikipedia.org/wiki/Prime_gap
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