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 243
- 243 is the first number of the form pq where p and q are a twin prime pair
- 243 is the smallest higher power that is a sum of two distinct higher powers (243 = 35 = 33 + 63)
- 243 is the smallest number n such that n and prime(n) end with the same two digits
- 243 is the only 3-digit number that is a fifth power
Common Properties of 243
The number n is called an apocalyptic power if 2n contains the consecutive digits 666 (in decimal).
A positive integer greater than 1 that is not prime is called composite.
Composite numbers are opposite to prime numbers.
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.
An integer n is powerful if for every prime p dividing n, p2 also divides n.
How much power? They all can be written as a2 b3.
The next Ulam number is uniquely the sum of two earlier distinct Ulam numbers.