How n (1+b) is not prime?

Question

Here is the complete proof taken from this link

How do I convince myself that n(1+b) is not prime when b>=1? Here is what I did: if n is 3 and b is 3. Then resulting string 111 111 is prime. Is this how it should be done it in proofs? The way I see is this. If n(1+b) is not proved for even one set of values then I can say it is not prime. Set of values in this case was n =3 & b = 3.

Is this approach of understanding poofs is right?

Answer 1

The number $n(1+b)$ is not prime because it has 2 divisors greater than 1. These are $(b+1)$ and $n$. I believe that's what is meant here.