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 89
- 89 is the smallest number for which the positive sum of all odd primes less than or equal to it is a square
- 89 is the first and only multi-digit prime p such that the sum of its digits powered to 1, 2, ... (as the position of the digit from left to right) is equal to p: 89 = 81 + 92
- 89 is the smallest prime that is a concatenation of pq and qp where p and q are prime
- 89 is the smallest prime with all digits containing holes
- 89 is the smallest prime whose digits are composites
- 89 is the only two-digit number that is the sum of its first digit and its second digit squared
Rare Properties of 89
Fibonacci numbers are numbers that form the Fibonacci sequence. The Fibonacci sequence is defined as starting with 1, 1 and then each next term is the sum of the two preceding ones.
Fibonacci numbers are very common in nature. For example, a pineapple has 8 spirals if you count one way, and 13 if you count the other way.
Common Properties of 89
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.