Your second questions concerns the gaps between semi primes.  It turns out that we can find infinitely many solutions to $$1\leq qp-rs\leq a$$ for all $a\geq 26$, and that under the [Elliott-Halberstam Conjecture][1], we can take $a\geq 6$


[In their work][2], Daniel A. Goldston, Sidney W. Graham, Janos Pintz and Cem Y. Yıldırım prove that if  $q_n$ is the $n^{th}$ almost prime, then $$\liminf_{n\rightarrow \infty} q_{n+1}-q_n \leq 26.$$

  [1]: http://en.wikipedia.org/wiki/Elliott%25E2%2580%2593Halberstam_conjecture
  [2]: http://arxiv.org/abs/math/0506067