6859. Cube root of 9999 is 21.54, so find the largest prime number less than that (19), then cube that number.
19^3=6,859
is obvious 6969
9409
961
773.
It can be 30 whose prime factors are 2, 3 and 5
67
The largest three digit prime number whose digits are all primes is 773.
The largest 3 digit number whose digits are all primes is 777. The largest 3 digit number with different prime digits is 753.
97969
9409
6859
961
7777
How about: 773
There is no three digit prime number whose square root is a prime number. Prime numbers have no factors other than 1 and themselves. Any number having a prime number as a square root is a composite number.
The answer is 961. The square root of 961 is 31, which is a prime number.
773.
73 satisfies your condition.