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 5

  • 5 is the smallest number of queens needed to attack every square on a standard chess board
  • 5 is the only prime which is the difference of two squares of primes
  • 5 is the only prime that is a member of 2 pairs of twin primes
  • 5 is the only number which is equal to the sum of all primes less than itself
  • 5 is the number of Platonic solids
  • 5 is the smallest degree at which polynomial roots are no longer findable in closed form
  • 5 is the smallest odd prime which is not a Gaussian prime (submitted by Sam Steingold)
  • 5 is the smallest number of vertices needed to create a non-planar graph
  • The only polygon that has the same number of sides and diagonals is a pentagon
  • 5 is the only number that is a member of two different pairs of twin primes

Rare Properties of 5

Automorphic (Curious)
Catalan
Fibonacci
Hungry
Narcissistic
Palindromic prime
Pentagonal

Common Properties of 5

Deficient
Evil
Odd
Palindrome
Prime
Square-free
Twin
Untouchable