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 1429
- 1429 is the smallest number whose square (2042041) has the first 3 digits the same as the next 3 digits
- 1429 is the lesser member p of the smallest cousin primes (p,p+4) such that p+1, p+2, and p+3 all have the same number of prime divisors (counted with multiplicity)
Common Properties of 1429
The number n is called an apocalyptic power if 2n contains the consecutive digits 666 (in decimal).
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.
A prime number is called a twin prime if there exists another prime number differing from it by 2.