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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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PragmaOnce
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    Yes. You've just defined it, in fact. You probably actually want some sort of formula for primes (q.v.) though. – Chris Eagle Jan 02 '12 at 16:46
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    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 02 '12 at 16:47
  • I updated my question to be more clear – PragmaOnce Jan 02 '12 at 16:53
  • I think Chris's wikipedia link should answer your question sufficiently. – Cam McLeman Jan 02 '12 at 16:57

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

user18063
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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 02 '12 at 16:55
  • Many functions exist. We just don't know of an extremely simple one. But the task is often implemented; it just requires finding and counting the primes until you reach n of them. – user3685427 Nov 28 '17 at 19:36