11

Definition
$11$ (Eleven) is:


 * The $5$th prime number after $2, 3, 5, 7$


 * The second repuint after the trivial case $1$


 * The only palindromic prime with an even number of digits


 * The smallest number which is the sum of a square and a prime in $3$ different ways:
 * $11 = 0^2 + 11 = 2^2 + 7 = 3^2 + 2$


 * The $7$th Ulam number after $1, 2, 3, 4, 6, 8$:
 * $11 = 3 + 8$


 * The $5$th Lucas number after $(2), 1, 3, 4, 7$:
 * $11 = 4 + 7$


 * A palindromic number whose square is also palindromic:


 * Cannot be represented by the sum of less than $6$ hexagonal numbers:
 * $11 = 6 + 1 + 1 + 1 + 1 + 1$


 * The first of $11$ primes of the form $2 x^2 + 11$:
 * $2 \times 0^2 + 11 = 11$


 * The $3$rd of $3$ primes of the form $2 x^2 + 3$:
 * $2 \times 2^2 + 3 = 11$

Also see

 * Divisibility by 11


 * 11 is Only Palindromic Prime with Even Number of Digits
 * Square of Small-Digit Palindromic Number is Palindromic