Java – prime factorization of large numbers

I want to find the prime factorization of large numbers less than 10 ^ 12

public static List<Long> primeFactors(long numbers) {
        long n = numbers;
        List<Long> factors = new ArrayList<Long>();
        for (long i = 2; i <= n / i; i++) {
            while (n % i == 0) {
                factors.add(i);
                n /= i;
            }
        }
        if (n > 1) {
            factors.add(n);
        }
        return factors;
    }

First, what is the complexity of the above algorithm? It's hard for me to find it?

It will also be too slow for numbers with large prime numbers

Is there a better algorithm, or how to optimize it?

Solution

If you want to decompose many large numbers, you might better find a prime number up to sqrt (n) (for example, use sieve of erasthenes) Then you must only check whether those primes are factors, not test all I < = sqrt (n)