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 8911
- 8911 is the largest 4-digit pseudoprime to base 2
- 8911 is the smallest Carmichael number that can't be represented as a sum of three squares
- 8911 is the smallest Carmichael number all of whose prime factors are congruent to 3 modulo 4
- 8911 is the smallest odd quarefree composite numbers n such that p-1 divides n-1 and p-1 does not divide (n-1)/2 for every prime factor of n
Rare Properties of 8911
The composite integer n is a Carmichael number if bn-1 = 1 (mod n) for every integer b
which is relatively prime with n.
Carmichael numbers behave like prime numbers with respect to the most useful primality test, that is they pretend to be prime.
Common Properties of 8911
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.
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 number is said to be square-free if its prime decomposition contains no repeated factors.
If you start with n points on a line, then draw n-1 points above and between, then n-2 above and between them, and so on, you will get a triangle of points. The number of points in this triangle is a triangle number.
Compare to square, pentagonal and tetrahedral numbers.