# Number Gossip

(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)

## Unique Properties of 729

- 729 is the largest 3-digit number in which the sum of digits is equal to the sum of prime factors
- Consecutive Smith numbers are called Smith brothers: 729 is the larger brother of the smallest pair of Smith brothers
- 729 is the smallest square with initial digit 7, while 7 is the last digit to appear as the first digit of a square
- 729 is the smallest square having last digit equal to the sum of the other digits
- 729 is the smallest cube k, such that k-1 is divisible by a non-trivial cube
- 729 is the smallest cube that is the concatenation of three numbers, one of which is the sum of the other two
- 729 is the smallest cube that is two plus a prime
- 729 is the only three-digit sixth power