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 83
- There are exactly 83 right-truncatable primes
- 83 is the smallest multi-digit prime consisting of only curved digits
- 83 is the smallest prime number which is the sum of a prime number of consecutive primes in a prime number of different ways (verified by Christopher Heckman)
- 83 is the smallest nontrivial integer whose square (6889) is a strobogrammatic number
- There are 83 squares with nine digits, all distinct
- There are 83 numbers n such that writing out 1 through n uses precisely n ones
Common Properties of 83
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.