Project Euler Solution using C#: Problem 25: 1000 Digit Fibonacci Number

Problem:

The Fibonacci sequence is defined by the recurrence relation:

Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.
Hence the first 12 terms will be:

F1 = 1
F2 = 1
F3 = 2
F4 = 3
F5 = 5
F6 = 8
F7 = 13
F8 = 21
F9 = 34
F10 = 55
F11 = 89
F12 = 144

The 12th term, F12, is the first term to contain three digits.
What is the first term in the Fibonacci sequence to contain 1000 digits? My Solution:

static void Main(string[] args)
{
    int count = 3;
 Dictionary F = new Dictionary();
 F.Add(0, 0);
 F.Add(1, 1);
 F.Add(2, 1);
 while (true)
 {
  BigInteger index1 = count - 1;
  BigInteger index2 = count - 2;
  BigInteger val = F[index1] + F[index2];
  F.Add(count, val);
  if (val.ToString().Length >= 1000)
  {
   break;
  }
  count += 1;
 }
 Console.WriteLine(count);
 Console.ReadLine();
}

Note: You can simplifies the coding :)