A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
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!
anonymous
 3 years ago
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!

This Question is Closed

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Furthermore, using Mathematica to algorithmically evaluate \(x\) by using arbitrarily large values of \(n\) does not converge to \(1\)!

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0* i love to know what is the answer

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0It's only necessary that someone links to a proof. I know I've seen this before, somewhere.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0This is called the prime number theorem.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0http://www.math.columbia.edu/~goldfeld/ErdosSelbergDispute.pdf

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Oh, wait, I found it in mathworld. Okay, thanks!

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0That's right. This is Legendre's constant. That's where I saw it before! http://en.wikipedia.org/wiki/Legendre%27s_constant

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Thanks for hte link, @eliassaab
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.