I don't get it. Is there a particular reason why prime number bases are further broken down via "+1"? And where do you stop with that? For example, "5" is not f

I don't get it. Is there a particular reason why prime number bases are further broken down via "+1"? And where do you stop with that? For example, "5" is not further broken down into 2^2+1. Edit: Oh, have not seen the drawings...