The smallest prime number in which all of the digits are also prime is 2.The smallest multi-digit prime number in which all of the digits are also prime is 23.
It is: 11 because 1+1 = 2 which is the smallest prime number
It is: 101
It is: 10007
It is 2 which also is the only even prime number
The smallest prime number, of course, is 2. The smallest prime number whose digits add up to 2 is, of course, 2. The next-smallest is 11. It is left as an exercise for the reader to determine whether the other numbers whose digits add up to 2 (e.g. 101, 1001, 10001) are prime.
The answer is 1. The smallest prime is 2 and the greatest prime (of however many digits) must be odd. The remainder of ANY odd number when divided by 2 must be 1.