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Java example source code file (Primes.java)

This example Java source code file (Primes.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

list, primes, util

The Primes.java Java example source code

/*
 * 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 <code>int:
 * <ul>
 * <li>primality test
 * <li>prime number generation
 * <li>factorization
 * </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);

    }

}

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