How many prime numbers in total are known as of November 2020?
Let’s head over to Wolfram|Alpha together.
Type in “Random 1000 digit prime”.
Wait a few seconds.
You should see something like this:
You can tap “More digits” to see more digits. Eventually you can observe all 1000 of them.
Congratulations! There is now one more known prime than there was a few seconds ago. And you are the only person who knows it!
Wait. How can I know this?
Well, strictly speaking, I can’t. It is possible that someone, somewhere, has hit upon that very prime you just discovered. But this is… shall we say, stupendously unlikely?
There are more than 10^{996} primes with a thousand decimal digits. The entire visible universe cannot store more than, oh, 10^{70} of them, if I’m being very generous. That means that the chances that your personal prime is or was already observed are less than one in 10^{900}, which is googol to the ninth power. I wouldn’t try to express that number using trillions and quadrillions. It’s like winning the finest prize of your country’s lottery, and then winning it again, and again, and again, a hundred times in a row.
So I think we can safely say that every time you or anyone else asks Wolfram|Alpha, or any other piece of software, for a random prime of decent size, there’s a new known prime. And this, as you may know, happens quite a few times per day, for various cryptographic reasons.
And therefore, there’s no such thing as “the number of known primes as of November 2020”. This isn’t an actual magnitude of anything meaningful.