# 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 3

- 3 is the greatest number of consecutive integers that can be pairwise relatively prime
- 3 is the only prime sandwiched between a prime and a composite number
- 3 is the only prime followed by a square
- Every positive integer is the sum of at most 3 triangular numbers
- If the n-th Fibonacci number is prime, then n must itself be prime, with the exception of 3, which is the 4th Fibonacci number
- 3 is the only number which is equal to the sum of all the natural numbers less than it
- 3 is the only triangular number that is also prime