# 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 15

- 15 is the smallest emirpimes
- 15 is the smallest composite cyclic number, that is number n with the property that there is only one group of order n
- 15 is the magic constant of the unique order-3 normal magic square
- 15 is the smallest number that equals the sum of numbers between its first and the second digits inclusive
- There are exactly 15 primes that are both left-truncatable and right-truncatable (deleting any number of digits at left or at right leaves a prime)
- 15 is the smallest product of twin primes
- The 15 theorem states that if a positive definite quadratic form with integer matrix represents all positive integers up to 15, then it represents all positive integers
- 15 is the only composite odd teenage number (submitted by Isaac LaComb)