Step by Step solution about How to resolve the algorithm Additive primes step by step in the Python programming language

Overview:

This Python code searches for "additive primes" below 500 and prints them. An additive prime is a prime number whose digits also form a prime number.

Detailed Explanation:

• is_prime Function:

  • This function checks if a given integer n is prime using the Sieve of Eratosthenes.
  • It handles the base cases (n <= 3) and eliminates even numbers.
  • It then iterates through potential prime divisors, using the optimizations that prime divisors come in the form of 6k +/- 1.
  • If n is divisible by any of the divisors, it returns False, indicating that n is not prime. Otherwise, it returns True.

• digit_sum Function:

  • This helper function calculates the sum of the digits of an integer n.
  • It loops through each digit in n by taking the modulo of 10, adding it to the sum, and dividing n by 10.
  • It returns the total sum of the digits.

• main Function:

  • The main function iterates through integers from 2 to 499 to search for additive primes.
  • For each i, it checks if it's prime using is_prime.
  • It also checks if the sum of the digits of i is a prime number using digit_sum and is_prime.
  • If both conditions are met, i is an additive prime, it is printed, and the count of additive primes is incremented.
  • Finally, it prints the total count of additive primes less than 500.

• if __name__ == "__main__": Block:

  • This is a standard Python idiom that ensures the main function is only called when the script is run as the main program (not imported).

def is_prime(n: int) -> bool:
    if n <= 3:
        return n > 1
    if n % 2 == 0 or n % 3 == 0:
        return False
    i = 5
    while i ** 2 <= n:
        if n % i == 0 or n % (i + 2) == 0:
            return False
        i += 6
    return True

def digit_sum(n: int) -> int:
    sum = 0
    while n > 0:
        sum += n % 10
        n //= 10
    return sum

def main() -> None:
    additive_primes = 0
    for i in range(2, 500):
        if is_prime(i) and is_prime(digit_sum(i)):
            additive_primes += 1
            print(i, end=" ")
    print(f"\nFound {additive_primes} additive primes less than 500")

if __name__ == "__main__":
    main()