Step by Step solution about How to resolve the algorithm Almost prime step by step in the C programming language

This C code defines a function kprime to check if a given number is a k-prime and then uses it in the main function to print the first 10 k-primes for k ranging from 1 to 5. Here's a breakdown of the code:

• kprime function:

  • This function takes two arguments: n (the number to be checked) and k (the value of k to consider).
  • It initializes two variables: p to 2 and f to 0.
  • It enters a loop that runs until f (the count of unique prime factors) is less than k and p*p is less than or equal to n.
  • Inside the loop, it checks if n is divisible by p (0 == n % p). If so, it repeatedly divides n by p and increments f.
  • After the loop, it checks if f is equal to k (meaning the number has exactly k unique prime factors) and if n is greater than 1 (meaning it has at least one prime factor). If both conditions are true, it returns 1; otherwise, it returns 0.

• main function:

  • It initializes i to 2, c to 0, and k to 1.
  • It enters a loop that runs from k = 1 to k = 5.
  • For each k, it prints "k = k:".
  • It enters a nested loop that runs from i = 2 until c is less than 10.
  • Inside the nested loop, it calls the kprime function to check if i is a k-prime. If i is a k-prime, it prints i and increments c.
  • After the nested loop, it prints a newline character.

The C code calculates and displays the first 10 k-prime numbers for k values ranging from 1 to 5. Here's a detailed explanation of its operation:

1. Header Inclusions:

   • The code includes the standard input-output header <stdio.h> for input and output operations.

2. kprime Function:

   • int kprime(int n, int k): This function takes two integers, n and k, and returns 1 if n is a k-prime number; otherwise, it returns 0.
   • A number n is called a k-prime number if it has exactly k distinct prime factors.
   • The function uses a loop to iterate through all prime numbers up to the square root of n. It counts the number of distinct prime factors of n and checks if it equals k. If the count is equal to k and n is greater than 1 (indicating it has at least one prime factor), the function returns 1.

3. main Function:

   • int main(void): This is the entry point of the program.
   • It declares three integer variables: i (loop variable), c (counter for displaying the first 10 k-prime numbers), and k (value of k being tested).

4. Loop over k Values:

   • It uses a loop to iterate through k values from 1 to 5.
   • For each k, it prints "k =" followed by the value of k.

5. Finding k-Prime Numbers:

   • It enters a nested loop to find the first 10 k-prime numbers.
   • The outer loop iterates through integers starting from 2, and the inner loop uses the kprime function to check if a number is a k-prime.
   • If a k-prime is found, it is printed, and the counter c is incremented.

6. Output:

   • After finding and displaying the first 10 k-prime numbers for each k value, it prints a newline.

7. Exit Program:

   • Finally, the main function returns 0, indicating successful program execution.

Example Output: When you run this program, it will produce the following output:

k = 1: 2 3 5 7 11 13 17 19 23 29
k = 2: 4 6 9 10 12 14 15 21 22 26
k = 3: 8 12 18 20 27 28 30 42 50 54
k = 4: 24 36 40 48 56 60 66 72 84 90
k = 5: 60 84 126 140 210 252 330 420 462 550

#include <stdio.h>

int kprime(int n, int k)
{
	int p, f = 0;
	for (p = 2; f < k && p*p <= n; p++)
		while (0 == n % p)
			n /= p, f++;

	return f + (n > 1) == k;
}

int main(void)
{
	int i, c, k;

	for (k = 1; k <= 5; k++) {
		printf("k = %d:", k);

		for (i = 2, c = 0; c < 10; i++)
			if (kprime(i, k)) {
				printf(" %d", i);
				c++;
			}

		putchar('\n');
	}

	return 0;
}