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 2047
- 2047 is the smallest Mersenne composite
- 2047 is the smallest strong pseudoprime to base 2
Rare Properties of 2047
A number of the form 2p - 1 is called a Mersenne number if p is prime.
It was believed many years ago, that all Mersenne numbers are prime. This is not so, thus there is a separate entry for Mersenne prime numbers.
Common Properties of 2047
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.
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.