# 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 41

- 41 is the smallest prime expressible as the sum of (at least two) consecutive primes in at least 2 ways
- 41 is the smallest prime that is not a difference between powers of 2 and 3 (submitted by Bruno Haible)
- 41 is the smallest non-palindromic prime which on subtracting its reverse gives a perfect cube (i.e., 41 - 14 = 3
^{3})
- 41 is the smallest half-quartan prime: p = (x
^{4} + y^{4})/2
- 41 is the smallest number such that the sum of its divisors equals 3 times its reverse (41 + 1 = 3*14)
- 41 is the first century with nine prime years

## Common Properties of 41

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.