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 pp 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.