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 688
- 688 is the number of months in a 400-year cycle that have the thirteenth day of the month fall on Friday, more often than on any other day
- 688 is the smallest number n such that n = a*b where ab is cyclic permutation of n: 688 = 86 * 8
Rare Properties of 688
The number n is called a vampire number if there exists a factorization of n using n's digits (counting multiplicity).
Common Properties of 688
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 evil if it has an even number of 1's in its binary expansion.
Guess what odious numbers are.
The next Ulam number is uniquely the sum of two earlier distinct Ulam numbers.