


'''simple docstring'''
import math
from collections.abc import Iterator
from itertools import takewhile


def       a				(      __a       )  ->     Tuple:



					'''simple docstring'''






					if 1 < number < 4:
										# 2 and 3 are primes
										return True
					elif number < 2 or number % 2 == 0 or number % 3 == 0:
										# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
										return False

					# All primes number are in format of 6k +/- 1
					for i in range(5			, int(math.sqrt(_lowercase       ) + 1       )			, 6       ):
										if number % i == 0 or number % (i + 2) == 0:
															return False
					return True


def       a				(      )  ->     List[str]:



					'''simple docstring'''






					UpperCamelCase__       :Any							 =			2
					while True:
										if is_prime(_lowercase       ):
															yield num
										num += 1


def       a				(      __a = 2000000       )  ->     Any:



					'''simple docstring'''






					return sum(takewhile(lambda __a       : x < n			, prime_generator()       )       )


if __name__ == "__main__":
		print(F"""{solution() = }""")









'''simple docstring'''
from __future__ import annotations

__snake_case											=					[True] * 1000001
__snake_case											=					2
while i * i <= 1000000:
		if seive[i]:
				for j in range(i * i, 1000001, i):
						__snake_case											=					False
		i += 1


def       a				(      __a       )  ->     bool:



					'''simple docstring'''






					return seive[n]


def       a				(      __a       )  ->     bool:



					'''simple docstring'''






					return any(digit in '''02468''' for digit in str(__a       )       )


def       a				(      __a = 1000000       )  ->     list[int]:



					'''simple docstring'''






					UpperCamelCase__       :Any							 =			[2]  # result already includes the number 2.
					for num in range(3			, limit + 1			, 2       ):
										if is_prime(__a       ) and not contains_an_even_digit(__a       ):
															UpperCamelCase__       :str							 =			str(__a       )
															UpperCamelCase__       :List[str]							 =			[int(str_num[j:] + str_num[:j]       ) for j in range(len(__a       )       )]
															if all(is_prime(__a       ) for i in list_nums       ):
																				result.append(__a       )
					return result


def       a				(      )  ->     int:



					'''simple docstring'''






					return len(find_circular_primes()       )


if __name__ == "__main__":
		print(F"""{len(find_circular_primes()) = }""")