d(d(x)) denotes the sum of digits of d(x).

For example, when x=(ABC)_{16}

Then, d(x) = (A)_{16}+(B)_{16}+(C)_{16} = (21)_{16}

and, d(d(x)) = 2 + 1 = 3

Consider the first 1011 (base ten) values of a *hexadecimal prime number* N.

Devise an algorithm such that:

• Each of d(N) and d(d(N)) is divisible by a prime power.

__Note__: A prime power is a number of the form p^{n}, where p is a prime number, and n is an integer greater than 1.