C# program to display prime numbers between given interval has been shown here. For example, the prime numbers between 10 and 20 are 11, 13, 17, 19. In this program, the upper and lower bounds of the interval are taken as inputs.

## 1. Algorithm to Display Prime Numbers between Given Interval

1. Take lower bound l and upper bound u as inputs.

2. For each number from l to u, check if it is a prime number.

3. If a number is prime, add it to a list of prime numbers.

4. Display the list after all the numbers within the interval have been checked.

## 2. Pseudocode to Display Prime Numbers between Given Interval

Input : Lower bound $l$ and Upper bound $u$

Output : Prime numbers between $l$ and $u$

1. Procedure primesBetweenInterval($l, u$):

2. Repeat for $n \in [l, u]$:

3. $flag \leftarrow 0$

4. Repeat for $i \in [2, \sqrt{n}]$:

5. If $n \mod i$ = 0:

6. $flag \leftarrow 1$

7. break

8. If $flag = 0$:

9. Print "$n$ is a prime"

10. End Procedure

## 3. Time complexity to Display Prime Numbers between Given Interval

Time Complexity: O($n\sqrt{n}$)

Here, $n$ is the number of elements between $l$ and $u$ inclusive

## 4. C# Program & output to Display Prime Numbers between Given Interval

Code has been copied
/********************************
alphabetacoder.com
C# program to display prime
numbers between given intervals
*********************************/

using System;

namespace AverageSum {
class Program {
// function to check prime
static bool check_prime(int num) {
// declare variables
int i;
// no prime number less than 2, so return false
if (num < 2)
return false;
// check divisibility of num
for (i = 2; i <= Math.Sqrt(num); i++) {
if (num % i == 0) {
return false; // num is composite so return false
}
}
// num is prime so return true
return true;
}

static void Main() {
// declare variables
int n1, n2, i;

// take input of the inteval
Console.Write("Enter the lower bound of interval = ");
Console.Write("Enter the upper bound of interval = ");

Console.Write("Prime numbers between " + n1 + " and " + n2 + ": ");
// find primes between n1 and n2
for (i = n1; i <= n2; i++) {
// check if current number is prime
if (check_prime(i)) {
Console.Write(i + " ");
}
}

// wait for user to press any key