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 1001
- 1001 is the smallest palindromic product of 3 consecutive primes
- 1001 is the smallest number containing 2 pairs of identical digits
- 1001 is the smallest number whose seventh power contains the same set of digits as another seventh power. Surprisingly, it is also the smallest number whose eighth power contains the same set of digits as another eighth power
Common Properties of 1001
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 odd if it is not divisible by 2.
Numbers that are not odd are even. Compare with another pair -- evil and odious numbers.
The number n is odious if it has an odd number of 1's in its binary expansion.
Guess what evil numbers are.
A palindrome is a number that reads the same forward or backward.
A number is said to be square-free if its prime decomposition contains no repeated factors.