The number of prime numbers - infinity

Take the largest prime number P_n. We prove there is a prime number greater than any prime P_n

 the sheer volume of numbers not exceeding primorial and not divisible by one of the prime numbers. Take any of these numbers, one of the two or is it a prime number is not included in these prime numbers or composite divisible by prime numbers are not included in these prime numbers. But that would be a composite number, you need to have the prime numbers are not included in these. Hence, no matter how large does not have a prime P_n, there is always a prime number greater than P_n.
Proved a prime number greater than any prime P_n. The number of prime numbers is infinite