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 functionimport 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)); }} |
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 methodimport 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)); }} |
17
Time complexity: O(1)
Space complexity: O(1)
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