Display Prime Numbers Between Two Intervals Using Functions in C++

A prime number is a number greater than 1 that has no divisors other than 1 and itself. For example, 2, 3, 5, 7, and 11 are prime numbers. In this article, we'll show you how to write a C++ program to display prime numbers between two intervals using function.

For example, given the interval from 0 to 50, we want to print all the prime numbers within this interval.

Input:
Starting interval: 0
Ending interval: 50

Output:
Prime numbers in the interval [0, 50] are:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47

Using Functions to Display Prime Numbers Between Two Intervals

To display prime numbers between two intervals, we use a function. A function is a piece of code that performs a specific task and helps keep the code cleaner and more reusable. Here's how we did it:

• First, we defined a function called primeNumbers() that takes two numbers as input, the lower and upper bounds.
• Next, inside this function, we use a loop to go through each number in the interval, skipping 0 and 1 as they are not prime.
• Then, for each number, we check if it is divisible by any number from 2 to half of that number. If not, we print it as a prime number.
• Finally, we call this function from the main() function and pass the interval values.

C++ Program to Display Prime Numbers Between Two Intervals Using Functions

Here's a complete C++ program where we used a function to print all prime numbers between two given intervals.

#include <iostream>
using namespace std;

// Function to print all prime numbers in the given interval
void primeNumbers(int lbound, int ubound) {
    int flag, i;
    while (lbound <= ubound) {
        flag = 0;

        // 0 and 1 are not prime
        if (lbound <= 1) {
            lbound++;
            continue;
        }

        // Check if current number is divisible by any number up to its half
        for (i = 2; i <= lbound / 2; i++) {
            if (lbound % i == 0) {
                flag = 1;  // Not a prime
                break;
            }
        }
        // If no divisor found, it's a prime
        if (flag == 0)
            cout << lbound << " ";

        lbound++;
    }
}

int main() {
    int lowerbound = 0, upperbound = 50;

    cout << "Starting interval: " << lowerbound << endl;
    cout << "Ending interval: " << upperbound << endl << endl;
    cout << "Prime numbers in the interval [" << lowerbound << ", " << upperbound << "] are: " << endl;    
    primeNumbers(lowerbound, upperbound);
    return 0;
}

The output below displays all prime numbers between the given intervals using function.

Starting interval: 0
Ending interval: 50

Prime numbers in the interval [0, 50] are: 
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 

Time Complexity: O(n^2) because for each number we check up to n/2 divisibility.

Space Complexity: O(1) because no extra space is used apart from a few variables.

Conclusion

In this article, we showed how to write a C++ program using functions to display prime numbers between two intervals. We created a function that checks and displays prime numbers within a specified range, with a time complexity of O(n^2) and space complexity of O(1).