PROJECT EULER #74

Link to Project Euler problem 74

The number 145 is well known for the property that the sum of the factorial of its digits is equal to 145:

1! + 4! + 5! = 1 + 24 + 120 = 145

Perhaps less well known is 169, in that it produces the longest chain of numbers that link back to 169; it turns out that there are only three such loops that exist:
169 -> 363601 -> 1454 -> 169
871 -> 45361 -> 871
872 -> 45362 -> 872
It is not difficult to prove that EVERY starting number will eventually get stuck in a loop. For example,
69 -> 363600 -> 1454 -> 169 -> 363601 (-> 1454)
78 -> 45360 -> 871 -> 45361 (-> 871)
540 -> 145 (-> 145)
Starting with 69 produces a chain of five non-repeating terms, but the longest non-repeating chain with a starting number below one million is sixty terms.
How many chains, with a starting number below one million, contain exactly sixty non-repeating terms?

This took too long (38 s) but I don't see any obvious optimisations (yet).

using System;
using System.Collections.Generic;

namespace ProjectEuler
{
    class Program
    {
        public static List<long> factorials = GenerateFactorials(9);
        static void Main()
        {
            //Problem 74
            DateTime start = DateTime.Now;
            int sixties = 0;
            for (int i = 1; i < 1000000; i++)
            {
                int count = 0;
                var cycle = new List<long>();
                long number = i;
                while (!cycle.Contains(number))
                {
                    count++;
                    cycle.Add(number);
                    number = GenerateSumOfFactorials(number);
                }
                if (count == 60)
                    sixties++;
            }
            Console.WriteLine(sixties);
            TimeSpan time = DateTime.Now - start;
            Console.WriteLine("This took {0}", time);
            Console.ReadKey();
        }
        public static List<long> GenerateFactorials(int n)
        {
            var factorialList = new List<long> { 1 };
            for (int i = 1; i <= n; i++)
            {
                long factorial = 1;
                for (int j = 1; j <= i; j++)
                    factorial *= j;
                factorialList.Add(factorial);
            }
            return factorialList;
        }
        public static long GenerateSumOfFactorials(long n)
        {
            string s = n.ToString();
            long sum = 0;
            for (int i = 0; i < s.Length; i++)
                sum += factorials[int.Parse(s.Substring(i, 1))];
            return sum;
        }
    }
}