# 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 10

• 10 is the base of our number system
• In base n, n is always written "10"
• 10 is the only semi-prime number with the property that the sum as well as the difference of its prime divisors are primes (2 + 5 = 7 and 5 - 2 = 3)
• 10 is the smallest noncototient, a number that can not be expressed as the difference between any integer and the total of coprimes below it
• 10 is the only number such that its binary representation is the concatenation of two copies of its decimal representation
• A square can be subdivided into 10 acute isosceles triangles, and 10 is the smallest such number
• The sequence of the last letters of the first ten numbers EOEREXNTEN ends in TEN
• 10 is the smallest nontrivial number that is both triangular and tetrahedral
• 10! is the only known factorial which is a product of two non-trivial factorials (10! = 6!7!) outside of the general pattern (n!)!=n!(n!-1)!
• 10 is the smallest number that equals the sum of primes between its smallest and largest prime factors, inclusive