Here's the question you clicked on:
badreferences
Prove that \(x\) is both rational and an integer.\[\lim_{n\to\infty}\left(\ln n-\frac{n}{\pi\left(n\right)}\right)=x\]The function \(\pi(n)\) counts the number of primes less than or equal to \(n\). I've seen this equation somewhere before, but I can't remember where. IIRC, \(x\) evaluates to \(1\). Mysterious!
Furthermore, using Mathematica to algorithmically evaluate \(x\) by using arbitrarily large values of \(n\) does not converge to \(1\)!
* i love to know what is the answer
i found something similar \[\lim_{n\to\infty}\frac{\pi(n)}{\frac{n}{\ln n}}=1\] http://en.wikipedia.org/wiki/Prime_number_theorem http://mathworld.wolfram.com/PrimeNumberTheorem.html
It's only necessary that someone links to a proof. I know I've seen this before, somewhere.
This is called the prime number theorem.
http://www.math.columbia.edu/~goldfeld/ErdosSelbergDispute.pdf
Oh, wait, I found it in mathworld. Okay, thanks!
That's right. This is Legendre's constant. That's where I saw it before! http://en.wikipedia.org/wiki/Legendre%27s_constant
Thanks for hte link, @eliassaab