I am trying to find a prime number between $n$ and $2n$.

I know that the number of primes between $n$ and $2n$ is $n/(2\ln n)$.

I was thinking of choosing a random number between $n$ and $2n$ and check if its prime. If no, repeat.

However, how do I find the repetitions needed to make sure I find a prime with a probability of .99?

Any help would be appreciated.