What does Terence Tao mean by the statement "primes behave randomly"? http://164.67.141.39:8080/ramgen/specialevents/math/tao/tao-20070117.smil
The Riemann hypothesis is, according to Tao, equivalent to the idea that the primes do behave randomly -- they are distributed according to the prime number theorem, with an error term that is exactly what you'd expect from the law of large numbers.
What does this mean? 
Edit: You need the latest RealPlayer for the link.
 A: I can't get your link to work. 
Suppose that for each positive integer $n$ you flip a coin that has probability $1/\log n$ of coming up "prime". Then the expected number of primes up to $n$ would be $n/\log n$. But there would be some variation around this expected value – some "error term". The size of the error term would be predicted by The Law of Large Numbers. And it would be the same as what's predicted for actual primes by the Riemann Hypothesis. 
A: The Riemann hypothesis is equivalent to the statement that, for all $\epsilon \gt 0$:
$\sum_{1 \le k \le n}{\lambda(k)} = O(n^{\frac{1}{2} + \epsilon})$
where $\lambda$ is the Liouville function, which takes values $\pm 1$ depending on whether its argument has an even or odd number of prime factors.  If instead of evaluating this function we were flipping a coin and counting heads as $+1$ and tails as $-1$, this is true almost surely by the law of the iterated logarithm.
A: I took it as a general statement, another professor said they were like weeds.  If you fill a wall with numbers and highlighted the prime numbers it would look random.  There are several pictures and charts even circles on the internet showing prime number relationships.
