Show that if p is prime and n < p 2n, then p|(27). Deduce that n(2n)-(n) < 2, and henc ((2n) - (n))/n < 2/lg n. (Since 2/1g nO as n, this shows that the density of primes between n and 2n decreases to- wards O, a weak form of the Prime Number Theorem.)