Project Euler 35 in Python

Question

I'm back with a Python solution for Project Euler 35. Any help would be appreciated; I generate the numbers by observing that all circular primes can only have digits 1, 3, 7, and 9. Then I use the Cartesian product built into itertools. I also have a local primes test from Wikipedia.

from primes import test as is_prime
from itertools import product # cartesian product
from timeit import default_timer as timer
def find_circular_primes_under(limit):
 def is_circular(digits):
 digits = list(digits)
 for digit in digits:
 if not is_prime(int(''.join(map(str, digits)))):
 return False
 else:
 digits.append(digits.pop(0))
 return True
 if type(limit) != int or limit <= 2:
 return "Error: primes are positive integers greater than 1."
 elif limit <= 11:
 sum = 0
 for k in range(limit):
 if is_prime(k):
 sum += 1
 return sum
 else:
 sum = 4
 for k in range(2, len(str(limit))):
 for combo in product([1, 3, 7, 9], repeat = k):
 if is_circular(combo):
 sum += 1
 return sum
start = timer()
ans = find_circular_primes_under(10**6)
elapsed_time = (timer() - start) * 1000 # s --> ms
print "Found %d in %r ms." % (ans, elapsed_time)

Answer 1

• Returning an error message instead of data is not a good approach to handling errors. Try and see what happens if you tweak your code to pass an invalid argument to find_circular_primes_under. Do you see your error message? No, the program raises an exception trying to format the return value as a number. It would be better to raise an appropriate exception instead of returning from the function.
• Modifying a container while iterating over it causes undefined behavior. In is_circular you could use for _ in xrange(len(digits)): instead of for digit in digits: to be safe. The digit variable is not used anyway.
• You could take advantage of collections.deque and its rotate method to produce the rotations.