/*
 * 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/**
 * 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.
/**
     * 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).
Params:
n – number to test.
Returns:
true if n is prime. (All numbers < 2 return false)./**
     * 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 &lt; 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.
Params:
n – a positive number.
Throws:
MathIllegalArgumentException – if n < 0.
Returns:
the smallest prime greater than or equal to 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 &lt; 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
Params:
n – number to factorize: must be ≥ 2
Throws:
MathIllegalArgumentException – if n < 2.
Returns:
list of prime factors of n/**
     * Prime factors decomposition
     *
     * @param n number to factorize: must be &ge; 2
     * @return list of prime factors of n
     * @throws MathIllegalArgumentException if n &lt; 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);

    }

}