




"""simple docstring"""





def        _UpperCamelCase     (      UpperCamelCase				)      ->      bool:


			"""simple docstring"""

			if p < 2:
						raise ValueError("p should not be less than 2!"				)
			elif p == 2:
						return True

			__UpperCAmelCase						:			List[Any]												=       4
			__UpperCAmelCase						:			Union[str, Any]												=       (1 << p) - 1
			for _ in range(p - 2				):
						__UpperCAmelCase						:			str												=       ((s * s) - 2) % m
			return s == 0


if __name__ == "__main__":
					print(lucas_lehmer_test(7))
					print(lucas_lehmer_test(11))






"""simple docstring"""



import math
from collections.abc import Iterator
from itertools import takewhile







def     __lowerCAmelCase		(		lowercase    :    int					)      ->		bool:


    """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     __lowerCAmelCase		(		)      ->		Iterator[int]:


    """simple docstring"""





    snake_case       : Optional[int]    =       2
    while True:
        if is_prime(lowercase					):
            yield num
        num += 1







def     __lowerCAmelCase		(		lowercase    :    int = 200_0000					)      ->		int:


    """simple docstring"""





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


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





