Understand the number 2^128 in three ways:

a. Use 1000 super computers (the fastest known today) to perform 2^128 bit operations. How many years would it take?

b. Suppose each atom can store one bit (0 or 1). Using all the atoms in the universe, could you store 2^128 bits? How many universes would you need?

c. Suppose you can break a cryptosystem with success probability 2^(128). How does this probability compare with the likelihood that you can win Powerball on each of five consecutive game days?

Please show any work