POWERS
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  In C, the largest integer is 2^31-1.  After that, what happens?

  Let's check in MATLAB.  I have heard that MATLAB uses 64 bits for 
data.  Does that mean 2^63-1 is the biggest integer?

  Make a table of the powers of 2, starting with:

    2^0 - 1 = 0
    2^1 - 1 = 1
    2^2 - 1 = 3
    2^3 - 1 = 7

  DEMONSTRATE LOOP
  DEMONSTRATE various ways of printing
  
  In MATLAB, things seem to be fine until we reach 2^63, when the result
is printed in scientific notation.  What does this mean?
(MATLAB defines values as real numbers.  The mantissa for real number is 
limited in length.)

  Notice that 2^54 seems to be equal to 2^54 - 1.  That can't be good!
(The mantissa is 53 bits long.  Now we have lost the units digit.)

  DEMONSTRATE USE OF MOD TO DISPLAY FINAL DIGITS

  If we really need to see the digits in numbers like 2^63, what can we do?
Is there any way to compute
2^222     = 6739986666787659948666753771754907668409286105635143120275902562304
and
2^222 - 1 = 6739986666787659948666753771754907668409286105635143120275902562303?

  USE VECTOR OF DIGITS