There is a special type of composite number called a ** Smith Number**, where the sum of its digits equals the sum of the digits of its prime factors. Note, all primes are trivial Smith Numbers.

For example, the number 94 is a ** Smith Number**. It has two prime factors: 94 = 2 x 47.

Sum of its digits: 9 + 4 = 13. Sum of the digits of its prime factors: 2 + 4 + 7 = 13

Find the first 8 Smith Numbers.

##### Smith Number Magic Square

This magic square is made up entirely of *Smith Numbers*.

What makes this particular magic square so interesting is that if we halve each of these Smith Numbers we have a Prime Magic Square.

The Magic Sum of the Smith Magic Square is 822, which is** not** a Smith Number.

The Magic Sum of the Prime Magic Square is 411, which is **not** a Prime number.

*Penrose Tiles to Trapdoor Ciphers (Martin Gardner 1989)*