A prime number 
is called circular if it remains prime after any cyclic
permutation of its digits. An example in base-10 is
because 
, 
, and 
are all primes. The first
few circular primes are 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131,
197, ... (OEIS A068652).
Base-10 circular primes not contain any digit 0, 2, 4, 5, 6, or 8, since having such a digit in the units place yields a number which is
necessarily divisible by either 
or 
(and therefore not prime).
Every prime repunit is a circular prime.
Circular primes are rare. Including only the smallest number corresponding to each cycle gives the sequence 2, 3, 5, 7, 11, 13, 17, 37, 79, 113, 197, 199, 337, 1193,
3779, 11939, 19937, 193939, 199933, ... (OEIS A016114;
Darling 2004), together with repunits 
, 
, 
, 
, 
, 
, and 
(the last several of which are probable
primes).
