A prime number is a positive integer greater than $1$ that has no positive divisors other than $1$ and itself.

For example, $2,3,5,7,11,13,17,$ and $19$ are prime numbers because they have no divisors other than $1$ and themselves.

Find the minimum positive integer b such that the number of prime numbers on the interval $[20000$; b$]$ inclusively equals to $20000.$