Java中的 BigInteger isProbablePrime() 方法及示例

Java.math.BigInteger.isProbablePrime(int certainty)方法用于判断此 BigInteger 是否可能是素数，或者它是否肯定是复合数。此方法在调用此方法的当前 BigInteger 上检查素数或复合数，并返回一个布尔值。如果这个 BigInteger 可能是素数，它返回 true，如果它肯定是复合的，则返回 false。如果确定性 <= 0，则返回 true。

句法：

public boolean isProbablePrime(int certainty)

参数：此方法接受强制性参数确定性，这是对用户可接受的不确定性的度量。这是因为 BigInteger 是一个非常非常大的数字，并且准确地确定它是否是素数非常困难且昂贵。因此，可以说这个方法根据一个阈值（1-1/2^确定性）检查这个 BigInteger 的素数。

返回值：此方法返回一个布尔值，说明此 BigInteger 是否为素数。如果这个 BigInteger 可能是素数，它返回 true，如果它肯定是复合的，则返回 false。

下面的程序用于说明 BigInteger 的 isProbablePrime() 方法。

示例 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);
    }
}

输出：

95848961698036841689418631330196 with certainty 1 false
95848961698036841689418631330196 with certainty 0 true
95848961698036841689418631330196 with certainty -1 true

示例 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);
    }
}

输出：

654561561356879113561 with certainty 1 false
654561561356879113561 with certainty 0 true
654561561356879113561 with certainty -1 true

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