Algorithm

1. Start
2. Read the lower limit (lower) and upper limit (upper) of the interval from the user.
3. Display "Prime numbers between [lower] and [upper] are:".
4. For each number i in the range from lower to upper:
   a. Initialize a boolean variable isPrime to true.
   b. If i is less than 2, set isPrime to false.
   c. For each number j in the range from 2 to the square root of i:
      i. If i is divisible by j, set isPrime to false and break the loop.
   d. If isPrime is true, display i as a prime number.
5. End

Code Examples

#1 Code Example- C++ programing Display Prime Numbers Between two Intervals

Code - C++ Programming

#include <iostream>
using namespace std;

int main() {

  int low, high, i;
  bool is_prime = true;

  cout << "Enter two numbers (intervals): ";
  cin >> low >> high;

  cout << "\nPrime numbers between " << low << " and " << high << " are: " << endl;

  while (low  <  high) {
    is_prime = true;

    // 0 and 1 are not prime numbers
    if (low == 0 || low == 1) {
      is_prime = false;
    }
 
    for (i = 2; i <= low/2; ++i) {
      if (low % i == 0) {
        is_prime = false;
        break;
      }
    }
        
    if (is_prime)
      cout << low << ", ";

    ++low;
  }

  return 0;
}
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Output

x
–
+
cmd
Enter two numbers (intervals): 0
20
Prime numbers between 0 and 20 are:
2, 3, 5, 7, 11, 13, 17, 19,

#2 COde Example- Display Prime Numbers When Larger Number is Entered first

Code - C++ Programming

#include <iostream>
using namespace std;

int main() {

  int low, high, temp, i;
  bool is_prime;
    
  cout << "Enter two numbers (intevals): ";
  cin >> low >> high;

  //swapping numbers if low is greater than high
  if (low > high) {
    temp = low;
    low = high;
    high = temp;
  }

  cout << "\nPrime numbers between " << low << " and " << high << " are:" << endl;

  while (low < high) {
    is_prime = true;


    if (low == 0 || low == 1) {
      is_prime = false;
    }

    for (i = 2; i <= low / 2; ++i) {
      if (low % i == 0) {
        is_prime = false;
        break;
      }
    }

    if (is_prime)
      cout << low << ", ";

    ++low;
  }

  return 0;
}
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Output

x
–
+
cmd
Enter two numbers (intervals): 20
0
Prime numbers between 0 and 20 are:
2, 3, 5, 7, 11, 13, 17, 19,
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Demonstration

C++ Programing Example to Display Prime Numbers Between Two Intervals-DevsEnv