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 35
- 35 = 23 + 33, i.e., the sum of the cubes of the first two primes
- There are 35 free (up to reflections and rotations) hexominoes, the polyominoes made from 6 squares
- 35 is the number of intersections of diagonals inside a regular heptagon
- The longest uncrossed knight's tour on a chessboard has 35 moves
Rare Properties of 35
A tetrahedral number is the number of balls you can put in a triangular pyramid.
This is the space generalization of triangular and square numbers.
Common Properties of 35
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.
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 number is said to be square-free if its prime decomposition contains no repeated factors.