[seqfan] Re: Maximal prime gaps

[Tomasz Ordowski]

Yes ...

Similar conjecture:

log log prime(n+1) - log log prime(n) < 1/n.

T. Ordowski

wt., 21 lut 2023 o 04:18 Trizen <trizenx at gmail.com> napisał(a):

> 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
> > ______________________
> > https://en.wikipedia.org/wiki/Prime_gap
> >
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> >
>
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