Sorry for the confusion, let me try to summarize the results a little bit for clarity.

1. The statement "If p and q are consecutive odd primes, then p+q has at least 3 factors in its prime factorization" is true (for any values of p and q). This is Example 3.8.
2. If we remove the word "consecutive" to get the statement "If p and q are odd primes, then p+q has at least 3 factors in its prime factorization", then this statement is false for some values of p and q. Of course if p and q are consecutive this is true, but, if p = 3 and q = 7, for example, 3+7=10 = 2*5 only has two primes in it's prime factorization.

Note we are only need one counterexample here. Others do exist, like p = 3 and q = 11 (with p+q=14=2*7), but sometimes there are at least 3 factors in the prime factorization even if p and q are not consecutive. For example, p = 5 and q = 11 with p+q = 16=2*2*2*2 has 4 factors in it's prime factorization.

Hope this helps a little!