Density of semiprimes on short intervals Perhaps this is a trivial question, but I'm not an expert. Let 
$$Q(m) = \bigl| \{ n : m\leq n \leq m + \log(m) \mbox{ and } n = p \cdot q\text{, where }p,q\text{ are prime} \} \bigr|$$
i.e., $Q(m)$ is the size of the set containing the numbers between $m$ and $m + \log(m)$ that are the product of two primes.
What is the value of the limit:
$$\lim_{m \rightarrow \infty} \frac{Q(m)}{\log(m)}$$

The expected size of $Q(m)$ is $\log\log m$ and so
$$
\liminf_{m\to\infty}\frac{Q(m)}{\log m}=0.
$$
I don't know that the $\limsup$ exists but it is probably 0.
