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 197
- 197 is the total sum of the digits of all two digit primes
- 197 is the smallest cyclic but not permutable prime (its cyclic rotations - 971 and 719 - are primes, but there exists a permutation - 791 or 917 - that is composite)
- 197 is the smallest multidigit number which is a sum of repdigits of its digits (197 = 111 + 9 + 77)
Common Properties of 197
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 prime is a positive integer greater than 1 that is divisible by no positive integers other than 1 and itself.
Prime numbers are opposite to composite numbers.
A number is said to be square-free if its prime decomposition contains no repeated factors.
A prime number is called a twin prime if there exists another prime number differing from it by 2.
The next Ulam number is uniquely the sum of two earlier distinct Ulam numbers.