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 problem41():
""" Pandigital prime
What is the largest n-digit pandigital prime that exists?
"""
for prime in mathhelper.prime_list(7654321, reverse=True):
if mathhelper.is_pandigital(prime):
return prime
def problem50():
""" Consecutive prime sum
Which prime, below one-million, can be written as the sum of the most consecutive primes?
"""
max_index = 0
biggest_prime = 0
for start in mathhelper.prime_list(1000000, reverse=True):
sum_primes = 0
for index, prime in enumerate(mathhelper.prime_list(start, reverse=True)):
if sum_primes > 1000000:
break
sum_primes += prime
if max_index < index and mathhelper.is_prime(sum_primes):
max_index = index
biggest_prime = sum_primes
return biggest_prime
def problem37():
""" Truncatable primes
Find the sum of the only eleven primes
that are both truncatable from left to right and right to left.
"""
found_item = 0
return_value = 0
for prime in mathhelper.prime_list(None):
if prime < 10:
continue
prime_text = str(prime)
for truncate in range(1, len(prime_text)):
left_part = int(prime_text[:(-1 * truncate)])
right_part = int(prime_text[truncate:])
if not mathhelper.is_prime(left_part) or not mathhelper.is_prime(right_part):
break
if truncate + 1 == len(prime_text):
return_value += prime
found_item += 1
if found_item == 11:
return return_value
def test_prime_list(self):
self.assertEqual(list(mathhelper.prime_list(-5)), [])
self.assertEqual(list(mathhelper.prime_list(-1)), [])
self.assertEqual(list(mathhelper.prime_list(0)), [])
self.assertEqual(list(mathhelper.prime_list(1)), [])
self.assertEqual(list(mathhelper.prime_list(2)), [2])
self.assertEqual(list(mathhelper.prime_list(3)), [2, 3])
self.assertEqual(list(mathhelper.prime_list(10)), [2, 3, 5, 7])
self.assertEqual(list(mathhelper.prime_list(17)), [2, 3, 5, 7, 11, 13, 17])
self.assertEqual(list(mathhelper.prime_list(18)), [2, 3, 5, 7, 11, 13, 17])
self.assertEqual(list(mathhelper.prime_list(19)), [2, 3, 5, 7, 11, 13, 17, 19])
self.assertEqual(list(mathhelper.prime_list(20)), [2, 3, 5, 7, 11, 13, 17, 19])
self.assertEqual(list(mathhelper.prime_list(21)), [2, 3, 5, 7, 11, 13, 17, 19])
self.assertEqual(list(mathhelper.prime_list(22)), [2, 3, 5, 7, 11, 13, 17, 19])
self.assertEqual(list(mathhelper.prime_list(23)), [2, 3, 5, 7, 11, 13, 17, 19, 23])
self.assertEqual(list(mathhelper.prime_list(24)), [2, 3, 5, 7, 11, 13, 17, 19, 23])
self.assertEqual(list(mathhelper.prime_list(-5, True)), [])
self.assertEqual(list(mathhelper.prime_list(-1, True)), [])
self.assertEqual(list(mathhelper.prime_list(0, True)), [])
self.assertEqual(list(mathhelper.prime_list(1, True)), [])
self.assertEqual(list(mathhelper.prime_list(2, True)), [2])
self.assertEqual(list(mathhelper.prime_list(3, True)), [3, 2])
self.assertEqual(list(mathhelper.prime_list(10, True)), [7, 5, 3, 2])
self.assertEqual(list(mathhelper.prime_list(17, True)), [17, 13, 11, 7, 5, 3, 2])
self.assertEqual(list(mathhelper.prime_list(18, True)), [17, 13, 11, 7, 5, 3, 2])
self.assertEqual(list(mathhelper.prime_list(19, True)), [19, 17, 13, 11, 7, 5, 3, 2])
self.assertEqual(list(mathhelper.prime_list(20, True)), [19, 17, 13, 11, 7, 5, 3, 2])
self.assertEqual(list(mathhelper.prime_list(21, True)), [19, 17, 13, 11, 7, 5, 3, 2])
self.assertEqual(list(mathhelper.prime_list(22, True)), [19, 17, 13, 11, 7, 5, 3, 2])
self.assertEqual(list(mathhelper.prime_list(23, True)), [23, 19, 17, 13, 11, 7, 5, 3, 2])
self.assertEqual(list(mathhelper.prime_list(24, True)), [23, 19, 17, 13, 11, 7, 5, 3, 2])
