Java Program to Display Prime Numbers Between Two Intervals

Introduction

Prime numbers are the building blocks of number theory, possessing unique properties and a host of applications in mathematics, computer science, and cryptography. A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. Identifying prime numbers between two intervals is a classic problem that tests basic programming skills and understanding of loops and conditional statements.

In this article, you will learn how to create a Java program that displays all prime numbers between two given intervals. This exercise will demonstrate efficient algorithm design, specifically focusing on handling edge cases and optimizing performance to handle larger ranges of numbers.

Java Program to Find Primes Between Intervals

Define the Method

1. Begin by defining a static method called printPrimeNumbersBetween that takes two integer parameters: the start and end of the interval.

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   public static void printPrimeNumbersBetween(int start, int end) {
       for (int i = start; i <= end; i++) {
           if (isPrime(i)) {
               System.out.print(i + " ");
           }
       }
       System.out.println();
   }
   

   This code iterates from start to end, checking each number to see if it's prime. If a number is prime, it prints the number followed by a space.

Implement the Prime Checking Method

1. Add the isPrime(int number) method which returns true if a number is prime.

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

   The isPrime method starts by ruling out numbers less than or equal to 1. It then checks divisibility from 2 up to the square root of the number. If any divisor is found, it returns false; otherwise, it confirms the number as prime.

Complete the Main Method

1. Incorporate a main method to run your program and test different intervals.

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   public static void main(String[] args) {
       int start = 10;
       int end = 50;
       System.out.println("Prime numbers between " + start + " and " + end + ":");
       printPrimeNumbersBetween(start, end);
   }
   

   This main method defines the start and end of the interval and calls the printPrimeNumbersBetween method. It provides output directly in the console for quick verification.

Conclusion

Developing a Java program to find prime numbers between two intervals allows you to practice with functions, loops, and mathematical logic. The approach discussed is efficient for moderate-sized intervals and can be easily adjusted for larger or different ranges. Use the above examples to further explore Java's capabilities and refine your programming techniques by experimenting with different optimization strategies or extending the functionality of the program. Remember, a deeper understanding of simple programs often leads to better insights in solving more complex problems in the future.