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 827
- 827 is the largest prime p with property that p2 is a concatenation of two 3-digit primes
- 827 is the smallest concube prime: it is the concatenation of the cubes of two consecutive numbers (these numbers are rare)
- 827 is the smallest twin prime such that both twins can be represented as a sum of a square and a cube (827 = 222+73 and 829 = 93+102)
Common Properties of 827
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.
A prime number is called a twin prime if there exists another prime number differing from it by 2.