If we knew the prime number counting function [tex] \pi(x) [/tex] then how could we recover the n-th prime?..of course an easy solution would be inverting this function [tex] \pi(x) [/tex] to get for integers the p-th prime..the question is..is there no other form of getting the nth prime by summing some values of the prime counting function over n or something similar i mean:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] P_{n}= \sum_{1}^{2^{n}} F(x, \pi(x) ) [/tex] how do you get this formulas?..thank you.

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# If you knew Pi(x) for every number

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