3. The largest known prime number is 2^82,589,933^_1, a number that is 24,862,048 digits long. Suppose you wrote that number out by hand. 

4. How many pieces of ordinary paper would you need and how long would it take?

5. There are infinitely many prime numbers. Illustrate the idea behind the proof of this theorem by assuming the only primes that exist are 2,3,5,7,11,13, and 17.