Is there anything one could say about in what region a prime number is guaranteed to be in? A general equation for $a$ and $b$, dependent on $n$, in $a<p_n<b$?
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2See here. – Wojowu Jan 08 '16 at 21:55
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How tight a range do you need? I mean you can always take $a=1$ and force $b$ to be so large that there's some easy way to prove it. I'd imagine $b=n^n$ or $n!$ would probably work. But that's a pretty weak result. What exactly do you need this for? – Gregory Grant Jan 08 '16 at 21:58
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Please search before asking. – Jan 08 '16 at 22:19
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There's always a prime between n and 2n. – fleablood Jan 08 '16 at 23:34
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And there is never a prime between n! + 2 and n! + n. – fleablood Jan 08 '16 at 23:35