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It is said that it is impossible to computationally find the nth prime number in at least O(logn) time complexity. Does there exist a mathematical proof to show this, or is it still an unsolved problem within mathematics? I would like to know if there is a way to computationally solve for the nth prime without solving for the n-1, n-2, ... prime. And if not, is there a proof showing that this is impossible.

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