Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
badreferences
Group Title
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!
 2 years ago
 2 years ago
badreferences Group Title
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!
 2 years ago
 2 years ago

This Question is Closed

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

mukushla Group TitleBest ResponseYou've already chosen the best response.4
* i love to know what is the answer
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.4
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
 2 years ago

badreferences Group TitleBest ResponseYou've already chosen the best response.0
It's only necessary that someone links to a proof. I know I've seen this before, somewhere.
 one year ago

eliassaab Group TitleBest ResponseYou've already chosen the best response.1
This is called the prime number theorem.
 one year ago

eliassaab Group TitleBest ResponseYou've already chosen the best response.1
http://www.math.columbia.edu/~goldfeld/ErdosSelbergDispute.pdf
 one year ago

badreferences Group TitleBest ResponseYou've already chosen the best response.0
Oh, wait, I found it in mathworld. Okay, thanks!
 one year ago

badreferences Group TitleBest ResponseYou've already chosen the best response.0
That's right. This is Legendre's constant. That's where I saw it before! http://en.wikipedia.org/wiki/Legendre%27s_constant
 one year ago

badreferences Group TitleBest ResponseYou've already chosen the best response.0
Thanks for hte link, @eliassaab
 one year ago
See more questions >>>
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.