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seen Sep 8 '12 at 10:19
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Apr
15
 awarded  Notable Question
Feb
20
 awarded  Popular Question
Dec
13
 awarded  Popular Question
Oct
26
 awarded  Yearling
Mar
15
 revised How can we show that $\pi (x+y) - \pi(y) \le \frac{1}{3} x + C$ using the sieve of eratosthenes?
added 1 characters in body
Mar
15
 comment How can we show that $\pi (x+y) - \pi(y) \le \frac{1}{3} x + C$ using the sieve of eratosthenes?
Yea, exactly TonyK.
Mar
15
 revised How can we show that $\pi (x+y) - \pi(y) \le \frac{1}{3} x + C$ using the sieve of eratosthenes?
deleted 114 characters in body
Mar
15
 revised How can we show that $\pi (x+y) - \pi(y) \le \frac{1}{3} x + C$ using the sieve of eratosthenes?
edited title
Mar
15
 accepted How can we show $\pi (2n) \ge \frac{\log \begin{pmatrix} 2n \\n \end{pmatrix} }{\log 2n}$
Mar
15
 comment How can we show $\pi (2n) \ge \frac{\log \begin{pmatrix} 2n \\n \end{pmatrix} }{\log 2n}$
Thanks, anon. So $\log m = \sum_{p\le 2n} \log p ord_{p}m \le \sum_{p\le 2n} \frac{\log 2n}{\log p} \log p \le \sum_{p\le 2n} \log 2n = \pi(2n)\log 2n $ , right ?
Mar
15
 accepted How can we show that $\operatorname{ord}_{p}\left(\binom{2n}n\right) \le \frac{\log 2n}{\log p}$
Mar
15
 comment How can we show that $\operatorname{ord}_{p}\left(\binom{2n}n\right) \le \frac{\log 2n}{\log p}$
Thanks, Ragib Zaman.
Mar
15
 comment How can we show that $\pi (x+y) - \pi(y) \le \frac{1}{3} x + C$ using the sieve of eratosthenes?
Thank you. The prime number theorem wasnt proven yet, so the only thing that comes in question is the sieve of eratosthenes (as TMM suggests, sieving n numbers in the interval of $y<n\le x+y$ but it looks like I did it wrong (I believe).
Mar
15
 asked How can we show $\pi (2n) \ge \frac{\log \begin{pmatrix} 2n \\n \end{pmatrix} }{\log 2n}$
Mar
15
 asked How can we show that $\operatorname{ord}_{p}\left(\binom{2n}n\right) \le \frac{\log 2n}{\log p}$
Mar
15
 revised How can we show that $\pi (x+y) - \pi(y) \le \frac{1}{3} x + C$ using the sieve of eratosthenes?
added 724 characters in body
Mar
15
 comment How can we show that $\pi (x+y) - \pi(y) \le \frac{1}{3} x + C$ using the sieve of eratosthenes?
I put my comment to your answer in the edit of my question, thanks.
Mar
14
 comment How can we show that $\pi (x+y) - \pi(y) \le \frac{1}{3} x + C$ using the sieve of eratosthenes?
Thanks for the correction dtldarek.
Mar
14
 revised How can we show that $\pi (x+y) - \pi(y) \le \frac{1}{3} x + C$ using the sieve of eratosthenes?
edited title
Mar
14
 asked How can we show that $\pi (x+y) - \pi(y) \le \frac{1}{3} x + C$ using the sieve of eratosthenes?
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