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 668
- 668 is the number of legal pawn moves in chess, as the moves are written in transcripts; that is, different captures are counted separately
- There are 668 palindromic primes with 7 digits
Common Properties of 668
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 odious if it has an odd number of 1's in its binary expansion.
Guess what evil numbers are.
The next Ulam number is uniquely the sum of two earlier distinct Ulam numbers.
The untouchable numbers are those that are not the sum of the proper divisors of any number.