https://www.gregmat.com/quizzes/quiz/prepswift-infinitude-of-primes (Question 4)
In the solution for Question4, the reasoning for why Option C is not possible is confusing. It says “Option C is not possible. If the successor could be prime, it can’t be the case that the successor could have a factor of a(raised to a), b(raised to b) or c(raised to c) - as that would mean that the successor isn’t prime.” But not all successors to numbers are prime, what then? Would this be possible if the successor to a number is composite? Would the more general fact and the right reasoning for this answer not be this: if a prime number divides x, it can never divide x+1 ?