I used Maple to factor (using ifactor) the number 10^128 + 1.  Maple produced the factors in a matter of seconds.

One of the factors had 116 digits.  I then restarted Maple and executed the command ifactor(X) where X was the

factor with 116 digits.  Maple found the number was prime instantly.  I do not understand how one can determine

that a number  with 116 digits is prime in less than a second.  My guess is that Maple has stored some large primes.

Also I used  Maple to factor (10^128+3) and I turned the program off because it was taking forever.