# 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 61

- The 61st Fibonacci number (2504730781961) is the smallest Fibonacci number which contains all the digits from 0 to 9
- 61 is the smallest multi-digit prime p such that the sum of digits of p
^{p} is a square
- 61 is the smallest prime whose reversal is a square
- 61 is the smallest number n such that the reversal of concatenation of the first n natural numbers is prime
- 61 is the smallest prime p such that p# is pandigital
- The earliest series of ten consecutive distinct digits of pi begin at the 61st digit

## Common Properties of 61

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.