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 2112
- 2112 is the only four-digit palindrome sandwiched between twin primes
- 2112 is the smallest palindrome which is a concatenation of n-th composite number with n
- 2112 is the smallest number that can be partitioned into three strings in more than one way, so that the product of three numbers is the partition divides n (2*11*2 and 2*1*12 divide 2112)
Common Properties of 2112
The number n is abundant if the sum of all its positive divisors except itself is more than n.
They are abundant above perfection, not to mention deficiency. See perfect and deficient numbers.
A positive integer greater than 1 that is not prime is called composite.
Composite numbers are opposite to prime 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.
One can take the sum of the squares of the digits of a number. Those numbers are happy for which iterating this operation eventually leads to 1.
A palindrome is a number that reads the same forward or backward.
The number n is practical if all numbers strictly less than n are sums of distinct divisors of n.
The next Ulam number is uniquely the sum of two earlier distinct Ulam numbers.