






from __future__ import annotations

import math

def      lowerCAmelCase__	(    _a       :			int    ):

		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(_a    ) + 1    )  ,      6    ):
				if number % i == 0 or number % (i + 2) == 0:
						return False
		return True

def      lowerCAmelCase__	(    _a       :			int    ):
		snake_case_				:							int						 =       str(_a    )
		snake_case_				:							Optional[int]						 =       [n]
		for i in range(1  ,      len(_a    )    ):
				list_nums.append(int(str_num[i:]    )    )
				list_nums.append(int(str_num[:-i]    )    )
		return list_nums

def      lowerCAmelCase__	(    _a       :			int    ):
		if len(str(_a    )    ) > 3:
				if not is_prime(int(str(_a    )[-3:]    )    ) or not is_prime(int(str(_a    )[:3]    )    ):
						return False
		return True

def      lowerCAmelCase__	(    _a       :			int = 11    ):
		snake_case_				:							list[int]						 =       []
		snake_case_				:							Union[str, Any]						 =       13
		while len(_a    ) != count:
				if validate(_a    ):
						snake_case_				:							List[Any]						 =       list_truncated_nums(_a    )
						if all(is_prime(_a    ) for i in list_nums    ):
								list_truncated_primes.append(_a    )
				num += 2
		return list_truncated_primes

def      lowerCAmelCase__	(    ):
		return sum(compute_truncated_primes(11    )    )


if __name__ == "__main__":
							print(F"""{sum(compute_truncated_primes(11)) = }""")








import math

def      lowerCAmelCase__	(    _a       :			int    ):

		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(_a    ) + 1    )  ,      6    ):
				if number % i == 0 or number % (i + 2) == 0:
						return False
		return True

def      lowerCAmelCase__	(    _a       :			float = 0.1    ):
		snake_case_				:							int						 =       3
		snake_case_				:							Optional[Any]						 =       3

		while primes / (2 * j - 1) >= ratio:
				for i in range(j * j + j + 1  ,      (j + 2) * (j + 2)  ,      j + 1    ):
						primes += is_prime(_a    )
				j += 2
		return j


if __name__ == "__main__":
							import doctest

							doctest.testmod()
