It can be proven that there is an infinite amount of prime numbe

Take any set of distinct positive integers, excluding the number one, to obtain (A, B, C, ...). Multiply all the values in that set to obtain X. X+1 cannot be a multiple of any number in that set, so there must be at least one prime number that is not contained in the set. Therefore, with a set of consecutive integers of any size in the form (2, 3, 4, ...), X+1 will always have a prime factor that is not included in the set, and therefore there exists an infinite number of primes.