Since each digit of a hyperprime must be prime, a hyperprime has only the digits $ 2,3,5,7$. Each of these as a one digit number works. For a two digit number of higher, $ 2$ or $ 5$ can only exist as the leftmost digit of the number. The part of the number after the first digit is a hyperprime as well, so first we will examine just the hyperprimes consisting of only $ 3$'s and $ 7$'s. We cannot have two consecutive $ 3$'s or two consecutive $ 7$'s, since neither $ 33$ nor $ 77$ is prime, so this number must alternate $ 3$'s and $ 7$'s. Also, we cannot have more than one $ 7$ because then the segment $ 737 = 11\cdot 67$ is not prime. Thus the possible hyperprimes using only $ 3$'s and $ 7$'s are: $ 3$ $ 7$ $ 37$ $ 73$ $ 373$. We can check easily that these are indeed hyperprimes. Now we consider adding a $ 2$ or $ 5$ before either of these. $ 23$ and $ 53$ are both hyperprimes, but adding a $ 2$ or a $ 5$ to any of the other hyperprimes listed above would make the sum of its digits divisible by $ 3$ (so the new number itself will be divisible by $ 3$, and hence not prime.) Thus all the hyperprimes are: $ 2,3,5,7,23,37,53,73,373$.