BigInteger isProbablePrime() Method in Java with Examples - GeeksforGeeks

03 Apr, 2019
The java.math.BigInteger.isProbablePrime(int certainty) method is used to tell if this BigInteger is probably prime or if it’s definitely composite. This method checks for prime or composite upon the current BigInteger by which this method is called and returns a boolean value. It returns true if this BigInteger is probably prime, false if it’s definitely composite. If certainty is <= 0, true is returned.
Syntax:
public boolean isProbablePrime(int certainty)
Parameters: This method accepts a mandatory parameter certainty which is a measure of the uncertainty that is acceptable to the user. This is due to the fact the BigInteger is a very very large number and finding exactly if it is prime is very difficult and expensive. Hence it can be said that this method checks for the prime of this BigInteger based on a threshold value (1 – 1/2certainty).
Return Value: This method returns a boolean value stating whether this BigInteger is prime or not. It returns true if this BigInteger is probably prime, false if it’s definitely composite.
Below program is used to illustrate the isProbablePrime() method of BigInteger.
Example 1:
// Java program to demonstrate// isProbablePrime() method of BigInteger  import java.math.BigInteger;  public class GFG {    public static void main(String[] args)    {          // Boolean variable to store the result        boolean result;          // Creates one BigInteger object        BigInteger a            = new BigInteger(                "95848961698036841689418631330196");          // When certainty is one,        // it will check number for prime or composite        result = a.isProbablePrime(1);        System.out.println(a.toString()                           + " with certainty 1 "                           + result);          // When certainty is zero,        // it is always true        result = a.isProbablePrime(0);        System.out.println(a.toString()                           + " with certainty 0 "                           + result);          // When certainty is negative,        // it is always true        result = a.isProbablePrime(-1);        System.out.println(a.toString()                           + " with certainty -1 "                           + result);    }}
95848961698036841689418631330196 with certainty 1 false
95848961698036841689418631330196 with certainty 0 true
95848961698036841689418631330196 with certainty -1 true

Example 2:
// Java program to demonstrate// isProbablePrime() method of BigInteger  import java.math.BigInteger;  public class GFG {    public static void main(String[] args)    {          // Boolean variable to store the result        boolean result;          // Creates one BigInteger object        BigInteger a            = new BigInteger(                "654561561356879113561");          // When certainty is one,        // it will check number for prime or composite        result = a.isProbablePrime(1);        System.out.println(a.toString()                           + " with certainty 1 "                           + result);          // When certainty is zero,        // it is always true        result = a.isProbablePrime(0);        System.out.println(a.toString()                           + " with certainty 0 "                           + result);          // When certainty is negative,        // it is always true        result = a.isProbablePrime(-1);        System.out.println(a.toString()                           + " with certainty -1 "                           + result);    }}
654561561356879113561 with certainty 1 false
654561561356879113561 with certainty 0 true
654561561356879113561 with certainty -1 true

Reference: https://docs.oracle.com/javase/9/docs/api/java/math/BigInteger.html#isProbablePrime(int)
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