A circular prime is a prime number 
that remains prime after any cyclic
permutation of its digits in a specified base.
An example in base 10 is 
because 
, 
, and 
are all primes. The first
few circular primes in base 10 are 2, 3, 5, 7, 11, 13, 17,
31, 37, 71, 73, 79, 97, 113, 131, 197, ... (OEIS A068652).
Circular primes with more than one digit in base 10 do not contain any of the digits 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 2 or 5 (and therefore not prime).
Every prime repunit is a circular prime.
Circular primes are rare. In base 10, 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). Further
examples are the repunits 
, 
, 
, 
, 
, 
, 
, which have all been proved prime.
Primality certificates for 
and 
are available from Enge (2026). The larger repunit 
remains a probable
prime, and is therefore a candidate circular prime
rather than a proved one.
