I'm thinking of a number, x, whose last 3 digits are somewhere between 400 and 500.
You could probably guess from those digits that it might be a square or a cube, but in fact it turns out to be both, and in fact the smallest possible such number.
What are the prime factors of x?
Extra credit: feeling adventurous, I next computed the smallest number, y, having the same last 3 digits, that was a seventh power, as well as a square and a cube.
What are the prime factors of y?