Java Program for Closest Prime Number

A prime number is a positive integer greater than 1 that is only divisible by 1 and itself.

Prime numbers are an essential concept in mathematics and computer science. They are integers that are only divisible by 1 and themselves. Finding prime numbers is an important task in many algorithms, and there are several methods to determine if a number is prime. One such problem is finding the closest prime number to a given number.

Here, we will explore how to find the closest possible prime number of any number.

Let's start!

For instance

Given integer number: 15

Closest prime number: 13

Algorithms

Algorithm-1

Step-1: Check if the input number is prime or not.

Step-2: If the input number is prime, the program prints the number and exits.

Step-3: If the input number is not prime, the program checks for the closest prime number by checking numbers before and after the input number.

Step-4: Use a brute-force approach to check if a number is prime by checking all numbers up to its square root.

Step-5: Print the closest prime number to the input number.

Algorithm-2

Step-1: Generate a list of prime numbers up to 2n using a sieve approach.

Step-2: Check for the closest prime number to the input number.

Step-3: Use a sieve approach to generate a list of prime numbers by eliminating all multiples of each prime number up to its square root.

Step-4: Check for the closest prime number by checking numbers above and below the input number in the list of prime numbers.

Step-5: Print the closest prime number to the input number.

Syntax

The Array.length method in Java returns the length of the given array.

Below refers to the syntax of it-

prime.lenght

Where, ‘prime' refers to an array.

Multiple Approaches

We have provided the solution in different approaches.

• By Using Brute-Force Approach

• By Using Sieve Approach

Let's see the program along with its output one by one.

Approach-1: By Using Brute-Force Approach

In this approach, an integer will be initialized in the program. Then by using brute-force approach finding the closest possible prime number.

Example

public class Main {
   // Function to check if a number is prime
   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;
   }
   public static void main(String[] args) {
      int n = 54;
      // Check if the input number is prime
      if (isPrime(n)) {
         System.out.println(n + " is a prime number.");
         return;
      }
      // Find the closest prime number by checking numbers above and below the input number
      int lower = n - 1;
      int upper = n + 1;
      while (true) {
         if (isPrime(lower)) {
            System.out.println(lower + " is the closest prime number to " + n + ".");
            return;
         } else if (isPrime(upper)) {
            System.out.println(upper + " is the closest prime number to " + n + ".");
            return;
         }
         lower--;
         upper++;
      }
   }
}

Output

53 is the closest prime number to 54.

Approach-2: Using a sieve approach

In this approach, an integer will be initialized in the program. Then by using sieve approach generate a list of prime number and then finding the closest possible prime number.

Example

import java.util.Arrays;
public class Main {
   // Function to generate a list of prime numbers up to a given limit
   static boolean[] sieve(int limit) {
      boolean[] prime = new boolean[limit+1];
      Arrays.fill(prime, true);
      prime[0] = false;
      prime[1] = false;
      for (int i = 2; i*i <= limit; i++) {
         if (prime[i]) {
            for (int j = i*i; j <= limit; j += i) {
               prime[j] = false;
            }
         }
      }
      return prime;
   }
   // Function to find the closest prime number to a given number
   static int closestPrime(int n, boolean[] prime) {
      int lower = n - 1;
      int upper = n + 1;
      while (true) {
         if (lower >= 0 && prime[lower]) {
            return lower;
         } else if (upper < prime.length && prime[upper]) {
            return upper;
         }
         lower--;
         upper++;
      }
   }
   public static void main(String[] args) {
      int n = 27;
      // Generate a list of prime numbers up to 2n
      boolean[] prime = sieve(2*n);
      // Find the closest prime number to n
      int closest = closestPrime(n, prime);
      System.out.println("The closest prime number to " + n + " is " + closest);
   }
}

Output

The closest prime number to 27 is 29

In this article, we explored different approaches to check closest prime number by using Java programming language.