PROJECT EULER #25

Link to Project Euler problem 25

The Fibonacci sequence is defined by the recurrence relation:

F_n = F_n-1 + F_n-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?

using System;
using System.Collections.Generic;

namespace ProjectEuler
{
   class Program
   {
       static void Main()
       {
           //Problem 25
           DateTime start = DateTime.Now;
           //again we use base 100000, saving the
           //chunks of the big number in a List<int>
           int digits = 0,carry=0,fibNo =2;
           var a = new List<int>{1};
           var b = new List<int>{1};
           var c = new List<int>();
           while (digits<1000)
           {
               fibNo+=1;
               //add the chunks carrying over to the next chunk
               for (int i = 0; i < b.Count; i++)
               {
                   int temp = a[i] + b[i] + carry;
                   int number;
                   carry =(Math.DivRem(temp, 100000, out number));
                   c.Add(number);
               }
               //if a has more chunks than b....
               if(a.Count>b.Count)
               {
                   c.Add(a[a.Count-1] + carry);
                   carry = 0;
               }
               //if the sum of a and b makes a new chunk...
               if (carry > 0)
               {
                   c.Add(carry);
               }
               //swap the numbers around
               b.Clear();
               foreach (int i in a)
               {
                   b.Add(i);
               }
               a.Clear();
               foreach (int i in c)
               {
                   a.Add(i);
               }
               c.Clear();
               //calculate how many digits, check the last chunk (MSB)
               //for less than 5 digits
               digits = a.Count*5;
               char[] ch = a[a.Count-1].ToString().ToCharArray();
               digits -= 5-ch.Length;
           }
           Console.WriteLine(fibNo + " has " + digits + " digits.");
           TimeSpan time = DateTime.Now-start;
           Console.WriteLine("This took {0}", time);
           Console.ReadKey();
       }
   }
}