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## '2009 Challenge' printed from http://nrich.maths.org/

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!