# 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 11

• 11 is the smallest prime such that 2p-1 is not prime
• 11 is the largest number which is not expressible as the sum of two composite numbers
• The first five rows of Pascal's triangle, when read left-to-right, form the first five powers of 11
• 11 is the smallest prime for which the sum of digits equals the number of digits
• 11 hexominoes can be folded into a cube
• 11 is the only prime comprising an even number of identical digits
• 11 is the smallest strobogrammatic prime
• 11 is the only palindromic prime with an even number of digits
• There are 11 convex uniform tilings (regular and semiregular) of the Euclidean plane. By symmetry there are 11 Archimedean (all edge lengths are the same, and all vertices look alike) tilings of the plane
• 11 is the only prime whose period length is two
• 11 divides all palindromes with an even number of digits
• The diagonals of a regular pentagon divide it into 11 regions
• 11 is the number of 2 by 2 binary matrices M such that M2 is also a binary matrix
• 11 is the smallest pandigital number in base 3: it is 102 in base 3 and contains all the possible digits
• 11 is the smallest prime with no prime digits
• 11 is the smallest multidigit number whose digital sum is prime
• 11 is the first prime repunit
• 11 is the smallest strong prime, aka a prime number that is greater than the arithmetic mean of its prime neighbors
• 11 is the largest known multiplicative persistence