How about: 777 or 753
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73 is the largest two-digit number that is prime and has prime numbers for both of its digits.
The largest 3 digit number whose digits are all primes is 777. The largest 3 digit number with different prime digits is 753.
73 is the largest 2 digit number that is both prime and has prime numbers for both of its digits.
The largest three digit prime number whose digits are all primes is 773.
As of October 2015, the largest known prime number is 2^57,885,161 − 1, a number with 17,425,170 digits.