Primes (Apache Commons Math 3.3 API)

org.apache.commons.math3.primes

## Class Primes

- java.lang.Object
- - org.apache.commons.math3.primes.Primes

-     public class Primes
      extends Object

  Methods related to prime numbers in the range of `int`:
  - primality test
  - prime number generation
  - factorization
  Since:
    3.2
  Version:
    $Id: Primes.java 1538368 2013-11-03 13:57:37Z erans $

- - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `static boolean` | `isPrime(int n)` Primality test: tells if the argument is a (provable) prime or not.
    `static int` | `nextPrime(int n)` Return the smallest prime greater than or equal to n.
    `static List<Integer>` | `primeFactors(int n)` Prime factors decomposition

    - ### Methods inherited from class java.lang.Object

      `clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

- - ### Method Detail

    - #### isPrime

          public static boolean isPrime(int n)

      Primality test: tells if the argument is a (provable) prime or not.

      It uses the Miller-Rabin probabilistic test in such a way that a result is guaranteed: it uses the firsts prime numbers as successive base (see Handbook of applied cryptography by Menezes, table 4.1).

      Parameters:
        `n` - number to test.
      Returns:
        true if n is prime. (All numbers < 2 return false).

    - #### nextPrime

          public static int nextPrime(int n)

      Return the smallest prime greater than or equal to n.
      Parameters:
        `n` - a positive number.
      Returns:
        the smallest prime greater than or equal to n.
      Throws:
        `MathIllegalArgumentException` - if n < 0.

    - #### primeFactors

          public static List<Integer> primeFactors(int n)

      Prime factors decomposition
      Parameters:
        `n` - number to factorize: must be ≥ 2
      Returns:
        list of prime factors of n
      Throws:
        `MathIllegalArgumentException` - if n < 2.

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