Java program to display prime numbers between given interval has been shown here. For example, the prime numbers between 30 and 50 are 31, 37, 41, 43, 47. 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. Java Program & output to Display Prime Numbers between Given Interval

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

import java.util.Scanner;
import java.lang.Math;

class Main {
// function to check prime
public boolean check_prime(int num) {
// declare variables
int i;
// no prime number less than 2, so return false
if (num < 2)
return false;
// check divisibility
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;
}

public static void main(String[] args) {
// declare instance of Scanner class
Scanner sc = new Scanner(System.in);

// declare object of Main class
Main obj = new Main();

// declare variables
int n1, n2, i;

// take input of the inteval
System.out.print("Enter the lower and upper bounds of interval = ");
n1 = sc.nextInt();
n2 = sc.nextInt();

System.out.print("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 it is prime, then print it
if (obj.check_prime(i)) {
System.out.print(i + " ");
}
}
}
}


Output

Enter the lower and upper bounds of interval = 100 150

Prime numbers between 100 and 150: 101 103 107 109 113 127 131 137 139 149 151