# Perfect primes (hard version) P43557

Statement

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The statement of this exercise is identical to that of exercise ‍. But here the solution required is more efficient in general.

Given a natural number n, let s(n) be the sum of the digits of n. In this exercise, we say that n is a perfect prime if the infinite sequence n, s(n), s(s(n)), …only contains prime numbers. For instance, 977 is a perfect prime, because 977, 9 + 7 + 7 = 23, 2 + 3 = 5, 5, …, are all prime numbers.

Write a recursive function that tells if a natural number n is a perfect prime or not.

Interface

 C++ bool is_perfect_prime(int n); C int is_perfect_prime(int n); Java public static boolean isPerfectPrime(int n); Python is_perfect_prime(n) # returns bool is_perfect_prime(n: int) -> bool

Precondition

We have n ≥ 0.

Observation You only need to submit the required procedure; your main program will be ignored.

Public test cases
• Input/Output

is_perfect_prime(977) → true
is_perfect_prime(978) → false
is_perfect_prime(0) → false
is_perfect_prime(11) → true
• Information
Author