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Is there a known mathematical equation to find the nth prime?

Is there a function, like f(n), I insert n into the function and it outputs nth prime number? I have been trying to find a pattern between the prime numbers, 1st differences, 2nd differences, but I can't find it.

To be clear: I want something like f(x)=x^2+5 or f(x)=2.sin(x)+x^2. You know what I mean...

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marked as duplicate by Charles, Ross Millikan, Chris Eagle, Zev Chonoles Jan 2 '12 at 17:00

This question was marked as an exact duplicate of an existing question.

Yes. You've just defined it, in fact. You probably actually want some sort of formula for primes (q.v.) though. – Chris Eagle Jan 2 '12 at 16:46
Sure. Let $f(n)$ be the function that inputs $n$ and outputs the $n$-th prime number. :) Less obnoxiously, you have to be more specific about the form of the function you're looking for. Closed-form expressions exist but are pretty computationally useless, usually relying on something like Wilson's theorem to function as a characteristic function for the primes. – Cam McLeman Jan 2 '12 at 16:47
I updated my question to be more clear – PragmaOnce Jan 2 '12 at 16:53
I think Chris's wikipedia link should answer your question sufficiently. – Cam McLeman Jan 2 '12 at 16:57

Well yes, the function $f$ does exist, but that doesn't mean we know what it looks like.

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It looks like {(1, 2), (2, 3), (3, 5), (4, 7), ...}. The OP no doubt intends a closed-form formula rather than a function, but that will depend on her/his definition of "closed-form". – Charles Jan 2 '12 at 16:55

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