


"""simple docstring"""






import math
from decimal import Decimal, getcontext



def 			A__		(					_UpperCAmelCase    :      int = 4_00_00_00	)							->	int:

	'''simple docstring'''


	try:
		snake_case__  :						Optional[Any]		=      int(_UpperCAmelCase	)
	except (TypeError, ValueError):
		raise TypeError("Parameter n must be int or castable to int."	)
	if n <= 0:
		raise ValueError("Parameter n must be greater than or equal to one."	)
	snake_case__  :						List[str]		=      1_00
	snake_case__  :						Tuple		=      (Decimal(5	) ** Decimal(0.5	) + 1) / Decimal(2	)

	snake_case__  :						str		=      (math.floor(math.log(n * (phi + 2)				,    _UpperCAmelCase	) - 1	) // 3) * 3 + 2
	snake_case__  :						List[str]		=      Decimal(round(phi ** Decimal(index + 1	)	)	) / (phi + 2)
	snake_case__  :						List[Any]		=      num // 2
	return int(_UpperCAmelCase	)


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







'''simple docstring'''


import math
from collections.abc import Generator
def 					__magic_name__(       UpperCAmelCase__ :       int	):
						UpperCamelCase_     :	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							,				UpperCAmelCase__	):
																		if (i % j) == 0:
																								break
												else:
																		yield i
def 					__magic_name__(       UpperCAmelCase__ :       int	):
						UpperCamelCase_     :	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)
												UpperCamelCase_     :	List[Any]					     =     int(math.sqrt(UpperCAmelCase__	)	) + 1
												for j in range(2							,				UpperCAmelCase__	):
																		if (i % j) == 0:
																								break
												else:
																		yield i
def 					__magic_name__(       UpperCAmelCase__ :       int	):
						UpperCamelCase_     :	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):
												UpperCamelCase_     :	Optional[int]					     =     int(math.sqrt(UpperCAmelCase__	)	) + 1
												for j in range(3							,				UpperCAmelCase__							,				2	):
																		# As we removed the even numbers, we don't need them now
																		if (i % j) == 0:
																								break
												else:
																		yield i
def 					__magic_name__(       ):
						from timeit import timeit

						UpperCamelCase_     :	int					     =     """from __main__ import slow_primes, primes, fast_primes"""
						print(timeit("""slow_primes(1_000_000_000_000)"""							,				setup=UpperCAmelCase__							,				number=1000000	)	)
						print(timeit("""primes(1_000_000_000_000)"""							,				setup=UpperCAmelCase__							,				number=1000000	)	)
						print(timeit("""fast_primes(1_000_000_000_000)"""							,				setup=UpperCAmelCase__							,				number=1000000	)	)


if __name__ == "__main__":
	__SCREAMING_SNAKE_CASE						=      int(input("Calculate primes up to:\n>> ").strip())
	for ret in primes(number):
		print(ret)
	benchmark()




