Define d(x) as sum of the digits of x, where x is a hexadecimal positive integer.
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 pⁿ, where p is a prime number, and n is an integer greater than 1.