PROJECT EULER #73

Link to Project Euler problem 73

Consider the fraction, n/d, where n and d are positive integers. If n < d and HCF(n,d)=1, it is called a reduced proper fraction.
If we list the set of reduced proper fractions for d <= 8 in ascending order of size, we get:

1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8

It can be seen that there are 3 fractions between 1/3 and 1/2.
How many fractions lie between 1/3 and 1/2 in the sorted set of reduced proper fractions for d <= 10,000?

Yet again a big thanks to my mentor: After trying to brute-force this by generating all the fractions using the a/b < c/d ...insert (a+c) /(b+d) if b+d = n, type of solution (I stopped the program after 40 mins) he suggested looking at this strategy (took 1.05 s):

using System;
using System.Collections.Generic;

namespace ProjectEuler
{
    class Program
    {
        static void Main()
        {
            //Problem 73
            DateTime start = DateTime.Now;
            int number =10000;
            var primeFactors = GeneratePrimeFactors(number);
            int max = 0,min=0,sum=0;
            for (int i = number; i > 3; i--)
            {
                int count = 0;
                max = (int) Math.Floor((decimal) i/2);
                min=(int)Math.Ceiling((decimal) i/3);
                for (int j = min; j <=max; j++)
                {
                    int test = primeFactors[i].Count;
                    foreach (int k in primeFactors[i])
                        if (j%k == 0)
                            test--;
                    if (test == primeFactors[i].Count)
                        count++;
                }
                sum += count;
            }
            Console.WriteLine(sum);
            Console.WriteLine();
            TimeSpan time = DateTime.Now - start;
            Console.WriteLine("This took {0}", time);
            Console.ReadKey();
        }
        public static List<List<int>> GeneratePrimeFactors(int n)
        {
            var primes = GeneratePrimes(n);
            var primeFactors = new List<List<int>> {new List<int> {0}};
            for (int i = 1; i <= n; i++)
                primeFactors.Add(new List<int>());
            if (n==1) return primeFactors;
            foreach (int i in primes)
                for (int j = i; j <= n; j += i)
                    primeFactors[j].Add(i);
            return primeFactors;
        }
        public static bool IsPrime(int n)
        {
            if (n < 2) return false;
            if (n == 2) return true;
            for (long i = 2; i <= Math.Sqrt(n); i++)
                if (n % i == 0) return false;
            return true;
        }
        public static List<int> GeneratePrimes(int n)
        {
            var primeNumbers = new List<int> { 2, 3 };
            for (int i = 5; i <= n; i += 2)
                if (IsPrime(i))
                    primeNumbers.Add(i);
            return primeNumbers;
        }
    }
}