Circular primes

J, 47 chars (w/ formatted output)

('nothing';'circular'){~*/1&p:".(|."0 1~i.&#)":

J, 23 chars (boolean only)

*/1&p:".(|."0 1~i.&#)":

": is a string conversion; i.&# produces a range of integers [0,len), and |."0 1~ is a rotation of the string by each successive integer of the range.

". converts the list of rotations back into numbers, 1&p: converts the list of numbers into booleans (i.e. "prime?" predicate), and */ is a multiply reduce over the booleans (i.e. and).

Python, 106 chars

p=input();n=`p`
for i in n:
 n=n[1:]+n[0];e=2
 while`e`!=n:p*=int(n)%e;e+=1
print'cniortchuilnagr'[p<1::2]

Mathematica 62 61

f@s_ := And @@ PrimeQ[FromDigits@StringRotateLeft[s, #] & /@ Range@9]

Usage

f["1193"]

True

f["11939"]

True

f["1456"]

False

f["193939"]

True

f["1111111"]

False

f["7"]

True

f["23"]

False