Proving the Formula for the n-th Prime Number using Number Theory

[eljose]

Hello i need help to prove the formula:

$$p_n =\sum_{k=2}^{2^{n}}[ |n/(1+ \pi (k))|^{1/n}]$$

where []=floor function and |x| the modulus of x...this appear in number theory to evaluate the n-th prime however i am not able to prove it...

 

[HallsofIvy]

So according to this formula, with n= 3, 2 is the third prime? I did not know that!

 

[Curious3141]

So according to this formula, with n= 3, 2 is the third prime? I did not know that!

Pure comedy!

 

[Curious3141]

Though in fact, that's 2^n at the top of the summation. Even then, something's wrong, I get the third prime as being three according to the summation. Need to check again since I rushed thru it, but it doesn't look right.