


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





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





def     _UpperCamelCase     ():






							"""simple docstring"""





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





def     _UpperCamelCase     (a__   :int = 200_0000       ):






							"""simple docstring"""





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


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











from math import ceil, sqrt





def     _UpperCamelCase     (a__   :int = 100_0000       ):






							"""simple docstring"""





							UpperCamelCase__				     =			0

							for outer_width in range(3   ,			(limit // 4) + 2       ):
														if outer_width**2 > limit:
																					UpperCamelCase__				     =			max(ceil(sqrt(outer_width**2 - limit       )       )   ,			1       )
														else:
																					UpperCamelCase__				     =			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() = }""")




