def problem35():
""" Circular primes
How many circular primes are there below one million?
"""
return_value = 0
for prime in mathhelper.prime_list(999999):
prime_digits = list(str(prime))
rotate_list = collections.deque(prime_digits)
rotate_list_length = len(rotate_list)
if rotate_list_length == 1:
return_value += 1
continue
if len({"0", "2", "4", "5", "6", "8"}.intersection(prime_digits)) > 0:
continue
for rotate in range(1, rotate_list_length):
rotate_list.rotate(1)
if not mathhelper.is_prime(mathhelper.create_number(rotate_list)):
break
if rotate + 1 == rotate_list_length:
return_value += 1
return return_value
def problem43():
""" Sub-string divisibility
Find the sum of all 0 to 9 pandigital numbers with this property.
"""
dividers = [1, 2, 3, 5, 7, 11, 13, 17]
return_value = 0
for permutation in itertools.permutations([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 10):
if permutation[0] == 0:
continue
divisibility = True
for start in range(1, 8):
three_digits = permutation[start:start + 3]
number = mathhelper.create_number(three_digits)
if number % dividers[start] != 0:
divisibility = False
break
if divisibility:
return_value += mathhelper.create_number(permutation)
return return_value
def test_create_number(self):
self.assertEqual(mathhelper.create_number(list("123")), 123)
self.assertEqual(mathhelper.create_number(list("0123")), 123)
self.assertEqual(mathhelper.create_number(list("9876")), 9876)
self.assertEqual(mathhelper.create_number([4, 5, 6, 7, 8, 9]), 456789)
