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/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math3.primes;

import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.util.LocalizedFormats;

import java.util.List;


/**
 * Methods related to prime numbers in the range of int:
 * 
    *
  • primality test
  • *
  • prime number generation
  • *
  • factorization
  • *
* * @since 3.2 */ public class Primes { /** * Hide utility class. */ private Primes() { } /** * 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). * * @param n number to test. * @return true if n is prime. (All numbers < 2 return false). */ public static boolean isPrime(int n) { if (n < 2) { return false; } for (int p : SmallPrimes.PRIMES) { if (0 == (n % p)) { return n == p; } } return SmallPrimes.millerRabinPrimeTest(n); } /** * Return the smallest prime greater than or equal to n. * * @param n a positive number. * @return the smallest prime greater than or equal to n. * @throws MathIllegalArgumentException if n < 0. */ public static int nextPrime(int n) { if (n < 0) { throw new MathIllegalArgumentException(LocalizedFormats.NUMBER_TOO_SMALL, n, 0); } if (n == 2) { return 2; } n |= 1;//make sure n is odd if (n == 1) { return 2; } if (isPrime(n)) { return n; } // prepare entry in the +2, +4 loop: // n should not be a multiple of 3 final int rem = n % 3; if (0 == rem) { // if n % 3 == 0 n += 2; // n % 3 == 2 } else if (1 == rem) { // if n % 3 == 1 // if (isPrime(n)) return n; n += 4; // n % 3 == 2 } while (true) { // this loop skips all multiple of 3 if (isPrime(n)) { return n; } n += 2; // n % 3 == 1 if (isPrime(n)) { return n; } n += 4; // n % 3 == 2 } } /** * Prime factors decomposition * * @param n number to factorize: must be ≥ 2 * @return list of prime factors of n * @throws MathIllegalArgumentException if n < 2. */ public static List primeFactors(int n) { if (n < 2) { throw new MathIllegalArgumentException(LocalizedFormats.NUMBER_TOO_SMALL, n, 2); } // slower than trial div unless we do an awful lot of computation // (then it finally gets JIT-compiled efficiently // List out = PollardRho.primeFactors(n); return SmallPrimes.trialDivision(n); } }





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