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 problem3():
""" Largest prime factor
What is the largest prime factor of the number 600851475143 ?
"""
const_number = 600851475143
for i in range(int(math.sqrt(const_number)), 2, -1):
if const_number % i == 0 and mathhelper.is_prime(i):
return i
def problem46():
""" Goldbach's other conjecture
What is the smallest odd composite
that cannot be written as the sum of a prime and twice a square?
"""
number = 33
while True:
number += 2
if mathhelper.is_prime(number):
continue
biggest_square = int(math.sqrt(number / 2))
for power in range(2, biggest_square + 1):
if mathhelper.is_prime(number - (2 * (power ** 2))):
break
if power == biggest_square:
return number
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 problem7():
""" 10001st prime
What is the 10 001st prime number?
"""
count = 0
number = 1
while True:
number += 1
if mathhelper.is_prime(number):
count += 1
if count == 10001:
break
return number
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 problem10():
""" Summation of primes
Find the sum of all the primes below two million.
"""
return sum(x for x in range(2, 2000000) if mathhelper.is_prime(x))
def test_is_prime(self):
self.assertEqual(mathhelper.is_prime(-5), False)
self.assertEqual(mathhelper.is_prime(-4), False)
self.assertEqual(mathhelper.is_prime(-3), False)
self.assertEqual(mathhelper.is_prime(-2), False)
self.assertEqual(mathhelper.is_prime(-1), False)
self.assertEqual(mathhelper.is_prime(0), False)
self.assertEqual(mathhelper.is_prime(1), False)
self.assertEqual(mathhelper.is_prime(2), True)
self.assertEqual(mathhelper.is_prime(3), True)
self.assertEqual(mathhelper.is_prime(4), False)
self.assertEqual(mathhelper.is_prime(5), True)
self.assertEqual(mathhelper.is_prime(6), False)
self.assertEqual(mathhelper.is_prime(7), True)