What steps would you follow to write a C program that finds prime numbers between two numbers?

Question Analysis

The question asks about the steps required to write a C program that finds all prime numbers between two given numbers. To address this, you need to have a clear understanding of the following:

1. Prime Number Definition: A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In other words, a prime number has no divisors other than 1 and itself.

2. Range: You need to find prime numbers between two given numbers, which involves iterating through this range and checking each number for primality.

3. Algorithm for Checking Primality: You'll need to implement an efficient method to check if a number is prime.

4. C Programming Basics: You should be familiar with basic C programming constructs such as loops, conditionals, and functions.

Answer

To write a C program that finds prime numbers between two numbers, you can follow these steps:

1. Initialize the Program:

   • Start by including necessary libraries such as stdio.h for input and output functions.

2. Define Main Function:

   • Create the main() function where you will implement the logic.

3. Input the Range:

   • Use scanf() to take two integer inputs from the user, representing the lower and upper bounds of the range.

4. Iterate Through the Range:

   • Use a for loop to iterate from the lower bound to the upper bound.

5. Check for Primality:

   • For each number in this range, check if it is a prime number.
   • To check primality, you can create a helper function isPrime(int num):
     • If num is less than 2, return false.
     • Loop from 2 to the square root of num. If num is divisible by any of these numbers, it is not prime.
     • If no divisors are found, return true.

6. Output Prime Numbers:

   • If a number is prime, print it to the console.

7. End the Program:

   • Return 0 to indicate successful execution.

Here's a sample implementation in C:

#include <stdio.h>
#include <math.h>

int isPrime(int num) {
    if (num < 2) return 0;
    for (int i = 2; i <= sqrt(num); i++) {
        if (num % i == 0) return 0;
    }
    return 1;
}

int main() {
    int lower, upper;
    printf("Enter two numbers (intervals): ");
    scanf("%d %d", &lower, &upper);

    printf("Prime numbers between %d and %d are: ", lower, upper);
    for (int i = lower; i <= upper; i++) {
        if (isPrime(i)) {
            printf("%d ", i);
        }
    }
    return 0;
}

This program effectively finds and prints all prime numbers within the given range by using a simple and efficient algorithm for checking primality.