Sunday Times Teaser 2512 – No Title

by Graham Smithers

Published November 14 2010 (link)

Using each of the digits 0 to 9 exactly once, I have written down two three-figure numbers and a four- figure number.

In no particular order, one of them is a perfect square, one is a perfect cube, and the other is a prime.

If I told you which of the square, the cube and the prime was the smallest then it would be possible for you to work out what those three numbers are.

What are they?