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

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)