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Quick ways to check for Prime and find next Prime in Java

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Many programming contest problems are somehow related Prime Numbers. Either we are required to check Prime Numbers, or we are asked to perform certain functions for all prime number between 1 to N. Example: Calculate the sum of all prime numbers between 1 and 1000000. Java provides two function under java.math.BigInteger to deal with Prime Numbers.

  • isProbablePrime(int certainty): A method in BigInteger class to check if a given number is prime. For certainty = 1, it return true if BigInteger is prime and false if BigInteger is composite. Below is Java program to demonstrate above function. 

Java




// A Java program to check if a number is prime using
// inbuilt function
import java.util.*;
import java.math.*;
 
public class CheckPrimeTest
{
    //Function to check and return prime numbers
    static boolean checkPrime(long n)
    {
        // Converting long to BigInteger
        BigInteger b = new BigInteger(String.valueOf(n));
 
        return b.isProbablePrime(1);
    }
 
    // Driver method
    public static void main (String[] args)
                         throws java.lang.Exception
    {
       long n = 13;
       System.out.println(checkPrime(n));
    }
}


Output

true

Time Complexity: O(1).

The time complexity of this algorithm is O(1), since the BigInteger.isProbablePrime() method takes constant time to check the primality of a number.

Space Complexity: O(1).

The space complexity of this algorithm is also O(1). We only use a single variable to store the number, which is constant space.

  • nextProbablePrime() : Another method present in BigInteger class. This functions returns the next Prime Number greater than current BigInteger. Below is Java program to demonstrate above function. 

Java




// Java program to find prime number greater than a
// given number using built in method
import java.util.*;
import java.math.*;
 
class NextPrimeTest
{
    // Function to get nextPrimeNumber
    static long nextPrime(long n)
    {
        BigInteger b = new BigInteger(String.valueOf(n));
        return Long.parseLong(b.nextProbablePrime().toString());
    }
 
    // Driver method
    public static void main (String[] args)
                    throws java.lang.Exception
    {
        long n = 14;
        System.out.println(nextPrime(n));
    }
}


Output

17

Time complexity: O(1)
Space complexity: O(1)

 



Last Updated : 28 Mar, 2023
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