C program to display the prime numbers in between two intervals

In C programming, finding prime numbers between two intervals is a common problem that involves checking each number in the range for primality. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Syntax

for(i = start + 1; i < end; i++) {
    flag = 0;
    for(j = 2; j <= i/2; j++) {
        if(i % j == 0) {
            flag = 1;
            break;
        }
    }
    if(flag == 0) {
        // i is prime
    }
}

Example 1: Display Prime Numbers Between Two Intervals

The following program finds and displays all prime numbers between two given intervals −

#include <stdio.h>

int main() {
    int number1, number2, i, j, flag;
    
    printf("Enter the two intervals: ");
    scanf("%d %d", &number1, &number2);
    
    printf("Prime numbers between %d and %d:
", number1, number2);
    
    for(i = number1 + 1; i < number2; i++) {
        flag = 0;
        
        // Check if number is prime
        for(j = 2; j <= i/2; ++j) {
            if(i % j == 0) {
                flag = 1;
                break;
            }
        }
        
        // If flag is 0, number is prime
        if(flag == 0 && i > 1)
            printf("%d
", i);
    }
    
    return 0;
}

Enter the two intervals: 10 50
Prime numbers between 10 and 50:
11
13
17
19
23
29
31
37
41
43
47

Example 2: Display Non-Prime Numbers Between Two Intervals

This program displays composite numbers (non-prime numbers) between two given intervals −

#include <stdio.h>

int main() {
    int number1, number2, i, j, flag;
    
    printf("Enter the two intervals: ");
    scanf("%d %d", &number1, &number2);
    
    printf("Non-prime numbers between %d and %d:
", number1, number2);
    
    for(i = number1 + 1; i < number2; i++) {
        flag = 0;
        
        // Check if number is prime
        for(j = 2; j <= i/2; ++j) {
            if(i % j == 0) {
                flag = 1;
                break;
            }
        }
        
        // If flag is 1, number is composite (non-prime)
        if(flag == 1)
            printf("%d
", i);
    }
    
    return 0;
}

Enter the two intervals: 10 20
Non-prime numbers between 10 and 20:
12
14
15
16
18

How It Works

• The outer loop iterates through each number in the given interval
• For each number, the inner loop checks divisibility from 2 to number/2
• If any divisor is found, the flag is set to 1 (composite number)
• If no divisor is found, the flag remains 0 (prime number)
• Numbers less than or equal to 1 are handled separately as they are not prime

Conclusion

Prime number detection between intervals uses a simple divisibility test with flag variables. The algorithm efficiently identifies prime and composite numbers by checking divisors up to half the number.