ACC's Math Conjecture II

Another one for posterity:

If N=31622777, then N^3 = 31622777796632428411433, and that's the largest N that has such a property.

I have tested this conjecture up to N's 100-digits long, and it holds true. Used the code below.
If you can find a larger N, let me know.
Thanks, ACC.

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Numerics;

namespace SquareStart
{
 class Program
 {
  static void Main(string[] args)
  {
            int power = Int32.Parse(args[0]);
   BigInteger factor = 1;
   BigInteger MAX = 1000000;
   BigInteger count = 0;
   for (BigInteger n = 1; ; n++, count++)
   {
    if (n % 10 != 0 && (BigInteger.Pow(n, power)).ToString().StartsWith(n.ToString()))
    {
     Console.WriteLine("{0} => {1}", n, BigInteger.Pow(n, power));
     BigInteger temp = n;
     n = 10 * n - factor;
     if (n <= temp)
     {
      n = temp;
     }
     else
     {
      factor *= 10;
     }
     count = 0;
    }
    if (count >= MAX)
    {
     n *= 10;
     count = 0;
     Console.Write("{0}-", n.ToString().Length);
    }
   }
  }
 }
}