When researching Goldbach's conjecture, I immediately came across a list of other unsolved problems in mathematics on wikipedia. Here is the link: http://en.wikipedia.org/wiki/Unsolved_problems_in_mathematics

There are so many different problems within each different mathematical concentration. Some we had talked about, like:

- Do any odd perfect numbers exist?
- Waring's Problem
- Goldbach's Conjecture

It still fascinates me that there are problems out there that are so old and have yet to be solved, even with today;s modern technology!

As far as Goldbach's conjecture, I think another intesting aspect is the fact that expressing a given even number as a sum of two primes is called a **Goldbach partition** of the number.

According to wikipedia, there is a partition function, "n number theory, a partition of a positive integer n is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered to be the same partition; if order matters then the sum becomes a composition. A summand in a partition is also called a part. The number of partitions of n is given by the **partition function p(n)**."

This is another function we can add to our list next to phi, mu, etc. Interesting!