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 683
- 683 is the smallest prime p such that p-3 and p+3 are divisible by a cube
- 683 is the smallest number n greater than zero that can be expressed as prime(product of digits of n) - (product of digits of n)
- 683 is the smallest prime that can be expressed as half of (the product of four different primes plus 1)
Common Properties of 683
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.
One can take the sum of the squares of the digits of a number. Those numbers are happy for which iterating this operation eventually leads to 1.
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.