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.

Click to reveal the answer.

Smith Numbers (4, 22, 27, 58, 85, 94, 121, 166)
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)