We were told M17 = 217 - 1 and M19 = 219 - 1 are prime numbers.

If this is true then the following two numbers should be perfect numbers:

216(217 - 1)

218(219 - 1)

The first number, when computed on my calculator, is 8589869056.

The second one is too large to be displayed on my 10-digit calculator.
However, I figure out that it is a 12-digit number starting with the digits 1374386913.

Why don't we guess the last two digits?