Number Choosing Contest.

Four

The sum of two and three

factorial(3)

The fifth positive nonzero prime

Two raised to the third power

4: breaks XYZ & 2, 3, 4 and 5.
5: breaks XY & 2, 3, 4 and 5.
6: breaks XYZ & 2, 3, 4 and 5.
7: breaks XY & 3, 4 and 5.
8: breaks XY & 2, 3, 4 and 5.

For the record, people are more than welcome to try numbers above a million if they think it'll be informative. You never know!