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







def      _a					(   lowercase__	:      int			):







     '''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					(   ):







     '''simple docstring'''


     SCREAMING_SNAKE_CASE__					:					Dict      =		2
     while True:
          if is_prime(lowercase__			):
               yield num
          num += 1







def      _a					(   lowercase__	:      int = 2_00_00_00			):







     '''simple docstring'''


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


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








"""simple docstring"""







from math import ceil, sqrt

def     UpperCAmelCase_					(				__a   :			int = 1_00_00_00						):




			'''simple docstring'''



			_lowerCamelCase					:					Tuple	       =    0

			for outer_width in range(3      ,							(limit // 4) + 2						):
						if outer_width**2 > limit:
									_lowerCamelCase					:					Optional[int]	       =    max(ceil(sqrt(outer_width**2 - limit						)						)      ,							1						)
						else:
									_lowerCamelCase					:					Any	       =    1
						if (outer_width - hole_width_lower_bound) % 2:
									hole_width_lower_bound += 1

						answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

			return answer


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





