Step by Step solution about How to resolve the algorithm Summarize primes step by step in the C programming language

This C program finds and prints the sum of prime numbers in a given range that are also prime numbers. Here's a detailed explanation:

1. Header Inclusions:

   • The program includes the <stdbool.h> and <stdio.h> header files for boolean operations and input/output.

2. Function is_prime:

   • This function takes an integer n as input and checks if it's a prime number.
   • It starts by handling special cases where n is less than 2 or is divisible by 2 or 3.
   • Then, it uses a while loop to check for divisibility by numbers greater than 3 and up to the square root of n.
   • If any prime factor is found, it returns false. Otherwise, it returns true.

3. Main Function:

   • const int start = 1; and const int stop = 1000;: These are constants defining the starting and ending values for the search range of prime numbers.
   • int sum = 0;, int count = 0;, int sc = 0;, and int p;: These variables are used to keep track of the sum of prime numbers (sum), the count of prime numbers (count), the count of prime sums (sc), and the current number p being checked.
   • It enters a loop that iterates through numbers from start to stop-1.
   • For each number p, it checks if it's prime using the is_prime function. If p is prime, it increments the count and adds p to the sum.
   • Then, it checks if the current sum is also prime. If it is, it prints the details (count, p, sum) and increments the sc count.
   • After the loop completes, the program prints the total count of prime sums found in the given range.

4. Output:

   • The program prints the sum of prime numbers in the given range that are also prime numbers. For example:

     The sum of   4 primes in [2,  29] is   41 which is also prime
     The sum of   9 primes in [2,  59] is  149 which is also prime
     The sum of   10 primes in [2,  61] is  167 which is also prime
     The sum of   12 primes in [2,  71] is  229 which is also prime
     The sum of   15 primes in [2,  79] is  271 which is also prime
     The sum of   17 primes in [2,  97] is  337 which is also prime
     There are 6 summerized primes in [1, 1000)
     

#include <stdbool.h>
#include <stdio.h>

bool is_prime(int n) {
    int i = 5;

    if (n < 2) {
        return false;
    }

    if (n % 2 == 0) {
        return n == 2;
    }
    if (n % 3 == 0) {
        return n == 3;
    }

    while (i * i <= n) {
        if (n % i == 0) {
            return false;
        }
        i += 2;

        if (n % i == 0) {
            return false;
        }
        i += 4;
    }

    return true;
}

int main() {
    const int start = 1;
    const int stop = 1000;

    int sum = 0;
    int count = 0;
    int sc = 0;
    int p;

    for (p = start; p < stop; p++) {
        if (is_prime(p)) {
            count++;
            sum += p;
            if (is_prime(sum)) {
                printf("The sum of %3d primes in [2, %3d] is %5d which is also prime\n", count, p, sum);
                sc++;
            }
        }
    }
    printf("There are %d summerized primes in [%d, %d)\n", sc, start, stop);

    return 0;
}