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 3137
- 3137 is the smallest four-digit prime that is comprised of two consecutive primes concatenated
- 3137 is the largest prime in which every substring is prime or 1
- 3137 is the smallest prime which is a concatenation of two primes in exactly three ways
Common Properties of 3137
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.
The number n is evil if it has an even number of 1's in its binary expansion.
Guess what odious numbers are.
One can take the sum of the squares of the digits of a number. Those numbers are happy for which iterating this operation eventually leads to 1.
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.