Congruence cases.

(1) Let b be the sum of two consecutive odd numbers that are primes (for example, b = 11 + 13). Prove that b has at least three prime factors (not necessarily different).

(2) Let b be the sum of two consecutive primes p and p', where p' > p >= 3 (for example, b = 89 + 97). Prove that b has at least three prime factors (not necessarily different).

Up for the challenge?