- #1
AxiomOfChoice
- 533
- 1
Let [itex]p_n[/itex] be the nth prime number. Can someone help me figure out how to show that
[tex]
\lim_{n\to \infty} \frac{\log (\log p_n)}{\log n} = 0.
[/tex]
You're allowed to assume that
[tex]
\lim_{n\to \infty} \frac{p_n}{n \log p_n} = 1.
[/tex]
I'm quite confident what I want to show is true, but it's hard to figure out how to do it because [itex]p_n > n[/itex] for every n. Thanks!
[tex]
\lim_{n\to \infty} \frac{\log (\log p_n)}{\log n} = 0.
[/tex]
You're allowed to assume that
[tex]
\lim_{n\to \infty} \frac{p_n}{n \log p_n} = 1.
[/tex]
I'm quite confident what I want to show is true, but it's hard to figure out how to do it because [itex]p_n > n[/itex] for every n. Thanks!