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 212
- 212 is the smallest even three-digit integer n such that n divided by the product of its digits is prime
- 212 is the only number whose 5-digit square has 4 identical digits: 2122 = 44944
- 212 is the smallest palindromic number with sum of digits prime and number of prime digits prime
Common Properties of 212
A positive integer greater than 1 that is not prime is called composite.
Composite numbers are opposite to prime numbers.
The number n is deficient if the sum of all its positive divisors except itself is less than n.
Compare with perfect and abundant numbers.
A number is even if it is divisible by 2.
Numbers that are not even are odd. Compare with another pair -- evil and odious numbers.
The number n is evil if it has an even number of 1's in its binary expansion.
Guess what odious numbers are.
A palindrome is a number that reads the same forward or backward.
Undulating numbers are numbers of the form abababab... in base 10.
This property is significant starting from 3-digit numbers, so we will not consider numbers below 100.