The Jargon File (version 4.4.7, 29 Dec 2003):

two-to-the-N
 quant.

    An amount much larger than N but smaller than infinity. ?I have
    2-to-the-N things to do before I can go out for lunch? means you probably
    won't show up.


The Free On-line Dictionary of Computing (30 December 2018):

two-to-the-N

   An amount much larger than N but smaller than infinity.
   "I have 2-to-the-N things to do before I can go out for lunch"
   means you probably won't show up.

   Numbers of the form two-to-the-N are very important in
   computing because they represent the value of bit N of a
   binary number (counting from 0) and the number of things you
   can count with an N bit number.

   [Jargon File]

   (1994-12-06)