This number is a composite.
66 is the lowest number that shares a strobogrammatic prime factor with its invertible partner, i.e., 66 and 99 are both divisible by 11. [Murton]
The smallest palindromic composite number n such that n^2+1 is prime. [Russo]
The number of primes less than 1259 that cannot be displayed on a 12-hour digital clock. [Fellows]
The smallest even number whose sum of distinct prime factors is a fourth power, this is curiously the fourth such number: 66 = 2 * 3 * 11 and 2 + 3 + 11 = 16 = 2^4. [Post]
The smallest number that can be expressed as a sum of two two-digit primes, each ending with the digit three, in two different ways (66 = 13 + 53 = 23 + 43). [Sladcik]
The smallest number that can be expressed as a sum of two primes in six different ways, i.e., 66=5+61=7+59=13+53=19+47=23+43=29+37. [Loungrides]
There are exactly 66 six-digit primes with distinct nonprime digits. [Bajpai]