Here's a Java program that displays prime numbers between two intervals:

import java.util.Scanner;

public class PrimeNumbers {
    
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        System.out.print("Enter the first number: ");
        int num1 = scanner.nextInt();
        System.out.print("Enter the second number: ");
        int num2 = scanner.nextInt();
        System.out.println("Prime numbers between " + num1 + " and " + num2 + " are: ");
        for (int i = num1; i <= num2; i++) {
            if (isPrime(i)) {
                System.out.print(i + " ");
            }
        }
    }

    public static boolean isPrime(int n) {
        if (n <= 1) {
            return false;
        }
        for (int i = 2; i <= Math.sqrt(n); i++) {
            if (n % i == 0) {
                return false;
            }
        }
        return true;
    }
}

Explanation:

The program prompts the user to enter two numbers using the Scanner class. The numbers are stored in the num1 and num2 variables, respectively.

The program then prints the message "Prime numbers between num1 and num2 are: " to the console.

The program then uses a for loop to iterate over all integers between num1 and num2. For each integer i, the isPrime function is called to check if i is a prime number. If it is, the value of i is printed to the console.

The isPrime function takes an integer n as its argument and returns a boolean value indicating whether n is a prime number or not. The function first checks if n is less than or equal to 1, in which case it returns false. If n is greater than 1, the function uses a for loop to check if n is divisible by any integer between 2 and the square root of n. If n is divisible by any of these integers, the function returns false. Otherwise, the function returns true.