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 1000
- 1000 is the smallest cube formed by concatenating other cubes
- 1000 = 103, as such it is the smallest product of three 2-digit numbers
- 1000 is the smallest number containing letter A when written out in American English
- 1000 is the smallest number whose scientific notation (1E3) is shorter than its decimal representation
- 1000 is the smallest cube of a non-palindromic number
Rare Properties of 1000
The number n is a cube if it is the cube of an integer.
Common Properties of 1000
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.
An integer n is powerful if for every prime p dividing n, p2 also divides n.
How much power? They all can be written as a2 b3.
The number n is practical if all numbers strictly less than n are sums of distinct divisors of n.