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 29
- The 29th power of two is the largest power of two to have all different digits
- 29 is the smallest multi-digit prime whose product of digits of its cube is also a cube
- 29 is the smallest multi-digit number which on adding its reverse gives a perfect square (i.e., 29 + 92 = 121 = 112)
- 29 is the largest number such that sum of its digits is greater than the number of primes up to it
- 29 is the smallest prime of form pp + 2
- 29 is the smallest prime equal to the sum of three consecutive squares: 29 = 22 + 32 + 42
- There are 29 distinct three-dimensional pentacubes (glued from five identical cubes by joining faces)
Common Properties of 29
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.
The n-th lazy caterer number is the maximum number of pieces a (circular) pizza can be cut into with n (straight-line) cuts.
Unlike the situation with cake, everybody gets the toppings.
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.
A prime number is called a twin prime if there exists another prime number differing from it by 2.