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 131
- The 131st Fibonacci number (1066340417491710595814572169) is the smallest Fibonacci prime which contains all the digits from 0 to 9
- 131 is the smallest number n such that n + 1 and n − 1 each has exactly 3 distinct prime factors
- 131 is the smallest Honaker prime: the sum of its digits equals the sum of the digits of its index (32) in the prime sequence
- 131 is the smallest prime that is a concatenation of a prime and its first digit
- 131 is the smallest palindromic prime made of only two digits such that swapping those digits creates another prime
- 131 is the smallest prime which stays prime when the end digits (on both sides) are repeated once (11311 is also prime)
- 131 is the smallest mountain prime
Common Properties of 131
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 palindrome is a number that reads the same forward or backward.
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.
The next Ulam number is uniquely the sum of two earlier distinct Ulam numbers.
Undulating numbers are numbers of the form abababab... in base 10.
This property is significant starting from 3-digit numbers, so we will not consider numbers below 100.