As of August 2017, the largest known Prime number is 2^74,207,281 − 1, a number with 22,338,618digits.
I attached a link with the 100 largest known prime numbers, there you can see the number of digits.
999,983
As of August 2017, the largest known prime number is 2^74,207,281 − 1, a number with 22,338,618digits.
It has been proven that there is no largest prime number, and therefore there exists a prime number, in fact, infinitely many, greater than 10^999999999 (having a billion digits); however, no humans have actually found a specific number of that size and identified it as prime.
The number 11 is prime and has two identical digits.
773.