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Are there any prime gap results like this

  1. Jul 28, 2006 #1

    uart

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    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 all n, 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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  3. Jul 28, 2006 #2

    shmoe

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  4. Jul 28, 2006 #3

    uart

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    Thanks, that was just what I was looking for but I didn't have a name to search on. I thought that someone would have postulated it before me. :)
     
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