Package cc.redberry.rings.primes

Class SmallPrimes

java.lang.Object

cc.redberry.rings.primes.SmallPrimes

public final class SmallPrimes
extends Object

Prime factorization of 32-bit integers. The code is taken from Apache Commons Math.

Since:

1.0

Method Summary

Modifier and Type	Method	Description
static int	boundedTrialDivision(int n, int maxFactor, gnu.trove.list.array.TIntArrayList factors)	Extract factors in the range PRIME_LAST+2 to maxFactors.
static boolean	isPrime(int n)	Primality test: tells if the argument is a (provable) prime or not.
static boolean	millerRabinPrimeTest(int n)	Miller-Rabin probabilistic primality test for int type, used in such a way that a result is always guaranteed.
static int	nextPrime(int n)	Return the smallest prime greater than or equal to n.
static int[]	primeFactors(int n)	Prime factors decomposition.
static int	smallTrialDivision(int n, gnu.trove.list.array.TIntArrayList factors)	Extract small factors.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

isPrime

public static boolean isPrime(int n)

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).

Parameters:

n - number to test.

Returns:

true if n is prime. (All numbers < 2 return false).

nextPrime

public static int nextPrime(int n)

Return the smallest prime greater than or equal to n.

Parameters:

n - a positive number.

Returns:

the smallest prime greater than or equal to n.

Throws:

IllegalArgumentException - if n < 0.

millerRabinPrimeTest

public static boolean millerRabinPrimeTest(int n)

Miller-Rabin probabilistic primality test for int type, used in such a way that a result is always guaranteed.

It uses the prime numbers as successive base therefore it is guaranteed to be always correct. (see Handbook of applied cryptography by Menezes, table 4.1)

Parameters:

n - number to test: an odd integer ≥ 3

Returns:

true if n is prime. false if n is definitely composite.

smallTrialDivision

public static int smallTrialDivision(int n,
                                     gnu.trove.list.array.TIntArrayList factors)

Extract small factors.

Parameters:

n - the number to factor, must be > 0.

factors - the list where to add the factors.

Returns:

the part of n which remains to be factored, it is either a prime or a semi-prime

boundedTrialDivision

public static int boundedTrialDivision(int n,
                                       int maxFactor,
                                       gnu.trove.list.array.TIntArrayList factors)

Extract factors in the range PRIME_LAST+2 to maxFactors.

Parameters:

n - the number to factorize, must be >= PRIME_LAST+2 and must not contain any factor below PRIME_LAST+2

maxFactor - the upper bound of trial division: if it is reached, the method gives up and returns n.

factors - the list where to add the factors.

Returns:

n or 1 if factorization is completed.

primeFactors

public static int[] primeFactors(int n)

Prime factors decomposition. Uses trial divisions (that is quite fast for ints).

Parameters:

n - number to factorize: must be ≥ 2

Returns:

list of prime factors of n

Throws:

IllegalArgumentException - if n < 2.

See Also:

BigPrimes.primeFactors(cc.redberry.rings.bigint.BigInteger)