The answers to the following question are found at http://www.forum.swarthmore.edu/dr.math/problems/purpose_zero.html

1. What good are perfect numbers?
2. Is zero prime, composite, or neither?
3. What is the difference between zero and nothing?
4. When something is divided by zero, why is the answer undefined?
5. What is infinity plus one?
6. Is infinity positive or negative?

At the address http://www.utm.edu/research/primes/mersenne.shtml#hist, you can find the history, theorems, and lists of Mersenne Primes. A prime number that can be written in the form 2ⁿ-1, where n is also prime, is said to be a Mersenne Prime. An interesting note is that the 25th and 26th Mersenne Primes were found by high school students Laura Laura Nickel and Curt Noll.