# 2009 Challenge

##### Stage: 3, 4 and 5 Challenge Level:

Many seemingly boring whole numbers are known to possess some curious property that actually makes them rather interesting. Examples of some interesting properties of numbers are
 Number Why is it interesting? $2$ It is the smallest prime. $28$ A perfect number: it is equal to the sum of its proper factors: $28 = 1+2+4+7+14$. $100$ $100=2^2$ in binary, $100=3^2$ in base $3$, $100=10^2$ in base $10$ and $100=n^2$ in base $n$ $230$ The total number of different symmetry structures crystals in three dimensions can exhibit. $541$ The hundredth prime number . $1089$ Take any 3 digit number whose digits are not all the same, reverse it and subtract from the first, take the new number and add its reverse. This will equals $1089$. $1729$ The smallest number expressible as the sum of two cubes in two different ways. $1999$ The smallest prime number such that the sum of its digits is a perfect number. $2^{43112609}-1$ The largest prime number known in $2008$.

The challenge is this:

## What is the most interesting mathematical fact or property of the number 2009 that you can discover?

You are encouraged to use spreadsheets or computers to look for interesting properties or to use the internet to search for connections in science. Be inventive! We would love to see some really creative ideas involving the number $2009$.

As this is an investigative problem, we shall wait until July to publish the best solutions, giving you plenty of time to think about it!