





'''simple docstring'''






import random







class       lowerCamelCase       :


					def __init__(       self						:	str							,  __snake_case						:	float							,  __snake_case						:	float							):





											'''simple docstring'''





											_snake_case: str	       =		x
											_snake_case: str	       =		y


					def  SCREAMING_SNAKE_CASE_		(       self						:	Optional[Any]							):





											'''simple docstring'''





											return (self.x**2 + self.y**2) <= 1




					@classmethod
					def  SCREAMING_SNAKE_CASE_		(       cls						:	Any							):





											'''simple docstring'''





											return cls(x=random.random()							,  y=random.random()							)





def    lowercase_   (		lowercase__    ) ->float:
						if number_of_simulations < 1:
												raise ValueError('At least one simulation is necessary to estimate PI.'    )

						_snake_case: int	       =		0
						for _ in range(lowercase__    ):
												_snake_case: int	       =		Point.random_unit_square()

												if random_point.is_in_unit_circle():
																		number_in_unit_circle += 1

						return 4 * number_in_unit_circle / number_of_simulations


if __name__ == "__main__":
		# import doctest

		# doctest.testmod()
		from math import pi

		A :			Dict							   =      'Please enter the desired number of Monte Carlo simulations: '
		A :			Optional[int]							   =      estimate_pi(int(input(prompt).strip()))
		print(F'An estimate of PI is {my_pi} with an error of {abs(my_pi - pi)}')












'''simple docstring'''






import math
from collections.abc import Generator





def    lowercase_   (		lowercase__    ) ->Generator[int, None, None]:
						_snake_case: Generator	       =		(i for i in range(1					,	(max_n + 1)    ))
						for i in (n for n in numbers if n > 1):
												for j in range(2					,	lowercase__    ):
																		if (i % j) == 0:
																								break
												else:
																		yield i





def    lowercase_   (		lowercase__    ) ->Generator[int, None, None]:
						_snake_case: Generator	       =		(i for i in range(1					,	(max_n + 1)    ))
						for i in (n for n in numbers if n > 1):
												# only need to check for factors up to sqrt(i)
												_snake_case: int	       =		int(math.sqrt(lowercase__    )    ) + 1
												for j in range(2					,	lowercase__    ):
																		if (i % j) == 0:
																								break
												else:
																		yield i





def    lowercase_   (		lowercase__    ) ->Generator[int, None, None]:
						_snake_case: Generator	       =		(i for i in range(1					,	(max_n + 1)					,	2    ))
						# It's useless to test even numbers as they will not be prime
						if max_n > 2:
												yield 2  # Because 2 will not be tested, it's necessary to yield it now
						for i in (n for n in numbers if n > 1):
												_snake_case: List[str]	       =		int(math.sqrt(lowercase__    )    ) + 1
												for j in range(3					,	lowercase__					,	2    ):
																		# As we removed the even numbers, we don't need them now
																		if (i % j) == 0:
																								break
												else:
																		yield i





def    lowercase_   (		) ->Optional[int]:
						from timeit import timeit

						_snake_case: Dict	       =		'from __main__ import slow_primes, primes, fast_primes'
						print(timeit('slow_primes(1_000_000_000_000)'					,	setup=lowercase__					,	number=100_0000    )    )
						print(timeit('primes(1_000_000_000_000)'					,	setup=lowercase__					,	number=100_0000    )    )
						print(timeit('fast_primes(1_000_000_000_000)'					,	setup=lowercase__					,	number=100_0000    )    )


if __name__ == "__main__":
		A :			List[str]							   =      int(input('Calculate primes up to:\n>> ').strip())
		for ret in primes(number):
				print(ret)
		benchmark()





