/*
* 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 java.util.List;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
/**
* Methods related to prime numbers in the range of <code>int</code>:
* <ul>
* <li>primality test</li>
* <li>prime number generation</li>
* <li>factorization</li>
* </ul>
*
* @since 3.2
*/
public class Primes {
/**
* Hide utility class.
*/
private Primes() {
}
/**
* Primality test: tells if the argument is a (provable) prime or not.
* <p>
* 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<Integer> 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<Integer> out = PollardRho.primeFactors(n);
return SmallPrimes.trialDivision(n);
}
}