Project Euler Problem 8, C#

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//Rextester.Program.Main is the entry point for your code. Don't change it
//Compiler version 4.0.30319.17929 for Microsoft (R) .NET Framework 4.5

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text.RegularExpressions;

namespace Rextester
{
    public class Program
    {
        
        static string digit_string = @"
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450";

public static void Main(string[] args)
        {
            digit_string = digit_string.Replace("\r\n", "");
            char[] digit_char_array = digit_string.ToCharArray();
            int[] digits = Array.ConvertAll(digit_char_array, c => (int)Char.GetNumericValue(c));
            
            long span = 13, last_i, i, j, product, max_product=1, max_product_i=0;
            
            last_i = (digits.Length - 1) - (span - 1);
            
            for (i=0; i<= last_i; i++)
            {
                for (j=i, product=1; j<=i+(span-1); j++)
                {
                    product *= digits[j];
                }
                
                if (product > max_product)
                {
                    max_product = product;
                    max_product_i = i;
                }
            }

Console.WriteLine("The max is: {0}, starting at position {1}", max_product, max_product_i+1);
        }
        
    }
}

Show compiler warnings [ + ] Show input
Compilation time: 0,12 sec, absolute running time: 0,09 sec, cpu time: 0,09 sec, average memory usage: 13 Mb, average nr of threads: 3