E 30. A Cryptarithm

Introduction: Here is a problem that I think would be good for any child who knows how to use the standard algorithm to do multi-digit multiplication. It is a cryptarithm from The Moscow Book of Puzzles, an amusing book by Boris Kordemsky, available in a very inexpensive Dover edition. For those of you who don't know (as I didn't) a cryptarithm is like a cryptogram, except the unknowns are digits, not letters. One you may have seen is (S  E  N  D) + (M  O  R  E) = (M  O  N  E  Y), where each letter stands for a digit, with different letters standing for different digits, and the expressions in parentheses standing for multi-digit numbers.

Problem: In the following multiplication, each * stands for a prime number digit (2, 3, 5, 7). Replace each * by a prime digit so that the multiplication is correct.

      * * *
     x  * *
   * * * *
 * * * *
* * * * *
Strangely enough, you have all the information you need to find the unique solution.