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 6857
- 6857 is the smallest prime of the form p3 - 2 where p is prime
- 6857 is the smallest 4-digit number n (out of two), such that the sum of the digit splits of n into two parts is equal to the product of the digits of n: (6 + 857) + (68 +57) + (685 + 7) = 6 * 8 * 5 * 7
Common Properties of 6857
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.
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.