(adsbygoogle = window.adsbygoogle || []).push({}); Are there any "prime gap" results like this ...

I was just reading about "prime gaps" and noticed that most of the results are asymptotic, as in "true if n is sufficiently large".

I was just wondering if there are any bounding results for prime gaps that are true for alln, p_n.

For example, take a conjecture like: [tex]p_{n} < p_{n+1} < 2 p_{n}[/tex]

Is something like that provable for all n. (not necessarily with the constant of "2", I just chose that as an example of what I meant).

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# Are there any prime gap results like this

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