# What is the smallest integer $n$ for which $\theta(n) > n$?

What is the smallest integer $n$ for which $\theta(n) > n$? Here $\theta(x) = \sum_{p \leq x} \log p$.

I googled around, checked some likely textbooks, and ran a program for $n \leq 10^7$, but didn't find it.

The integer and a reference would be nice.

Thanks.

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Well, assuming there is such a thing. The first number for which $\mbox{Li} x$ and $\pi(x)$ change places is almost $10^{400}$ –  Will Jagy Jan 25 '13 at 2:16
@RClark Wikipedia has some good information on the number Will refers to: en.wikipedia.org/wiki/Skewes%27_number –  Matthew Conroy Jan 25 '13 at 3:02
@MatthewConroy: Thanks, I found that. –  RClark Jan 25 '13 at 18:13
@WillJagy Such a number does exist by Littlewood's Oscillation Theorem for $\theta(x)$. –  RClark Jan 25 '13 at 18:14
This function is most commonly written $\vartheta$ with \vartheta. –  lhf May 6 '13 at 17:34