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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:
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:
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); } }