Proving two consecutive odd primes have at least 3 prime divisors.

Question

Prove that the sum of two consecutive odd primes has at least three prime divisors (not necessarily different).

Answer 1

Well, if $P$ and $Q$ are consecutive odd primes, then $P+Q$ is even, so $2$ divides $P+Q$. Hence, $P+Q=2R$, for some $R$. If $R$ were prime, then $R$ were a prime between $Q$ and $P$, a contradiction.