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 71
- 71 is the only two-digit number n such that (nn − n!)/n is prime
- 71 is the largest of the supersingular primes, i.e., the set of primes that divide the group order of the Monster group
- 7! + 1 = 71^n. Moreover, 71 is the largest known number n such at its square is 1 plus a factorial
- 713 = 357911: the concatenation of five consecutive primes
Rare Properties of 71
The n-th Google number is the first n-digit prime found in the decimal expansion of e.
They are named Google numbers because of the unusual hiring ad that Google put up.
Common Properties of 71
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.