How many prime numbers are known?

Wikipedia says that the largest known prime number is $2^{43,112,609}-1$ and it has 12,978,189 digits. I keep running into this question/answer over and over, but I haven’t been able to find how many known prime numbers exist. The website primes.utm.edu allows downloading of the first 50,000,000 known primes so I know there are at least that many; I’m not expecting to find a list of all known primes, but is there any information on how many there are known?

edit Relevant video from Khan Academy: Prime Number Theorem: the density of primes