# 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
• 5 is the smallest number that appear in two twin Pythagorean triplets (3, 4, 5) and (5, 12, 13)
• John Conway proved that in the Conway's Soldiers game, no finite sequence of moves allows a soldier to advance to the fifth row above the horizontal line.
• The volume of a unit ball reaches its maximum in dimension 5.