Please use C++ to write these 3 methods, also the algorithm for sieve is below the code.

private: bool const is_prime_; const int limit_; int num_primes_, max_prime_; int count num_primes() const ( /TODO: write code to count the number of primes found int num_digits(int num) const f I TODO: write code to determine how many digits are in an integer //Hint: No strings are needed. Keep dividing by 10 void sieve) /I TODO: write sieve algorithm 1