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 199
- 199 is the smallest number with an additive persistence of 3
- 199 is the smallest prime which can be partitioned into three parts such that the last part is the product of the first two
- 199 is the smallest non-cubic number whose fifth power is closer to a cubic number than a square number
- 199 is the smallest multidigit prime such that its largest digit is equal to the largest digit of the sum of its digits
Common Properties of 199
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 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.