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 1423
- 1423 is the smallest prime number that can be formed by concatenating the first several positive integers
- 1423 is the smallest prime containing 2n digits in which the sum of the first n digits equals that of the rest
- 1423 is the smallest prime with nonzero digits such that sum of the cubes of its digits equals the square of the sum of its digits (13+43+23+33 = (1+4+2+3)2)
Common Properties of 1423
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 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.