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 123
- 123 is the smallest semiprime which is the concatenation of the numbers 1 through n for some n
- 123 is the smallest squarefree number whose external as well as internal digits form a squarefree number
- Start with any number, then write out the number of even digits followed by the number of odd digits followed by the total number of digits. After a finite number of repetitions the result will be 123
Common Properties of 123
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.
The number n is evil if it has an even number of 1's in its binary expansion.
Guess what odious numbers are.
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.
A number is said to be square-free if its prime decomposition contains no repeated factors.