Prime

If you know the prime factorization of n, can you use that to tell anything about the prime factorization of n+1?

>>3
And more generally, for a + b = n, all integral factors common to a and b must be in n, and no factor of one but not the other can be in n.
The disappearence of prime factors through addition of numbers is a pretty mundane thing, but their appearence is mysterious and magical.