/// Prime factors decomposition
///
/// @param n number to factorize: must be ≥ 2
/// @return list of prime factors of n
/// @; 2.
public static List <int> primeFactors(int n)
{
if (n < 2)
{
throw new ArgumentException(); // 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));
}
/// 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 bool isPrime(int n)
{
if (n < 2)
{
return(false);
}
foreach (int p in SmallPrimes.PRIMES)
{
if (0 == (n % p))
{
return(n == p);
}
}
return(SmallPrimes.millerRabinPrimeTest(n));
}