



import math
from collections.abc import Generator


def 						UpperCAmelCase__   (   UpperCAmelCase__			:int       ):






 '''simple docstring'''

 a							=		(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 						UpperCAmelCase__   (   UpperCAmelCase__			:int       ):






 '''simple docstring'''

 a							=		(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)
  a							=		int(math.sqrt(UpperCAmelCase__       )       ) + 1
  for j in range(2			,       UpperCAmelCase__       ):
   if (i % j) == 0:
    break
  else:
   yield i


def 						UpperCAmelCase__   (   UpperCAmelCase__			:int       ):






 '''simple docstring'''

 a							=		(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):
  a							=		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 						UpperCAmelCase__   (   ):






 '''simple docstring'''

 from timeit import timeit

 a							=		"from __main__ import slow_primes, primes, fast_primes"
 print(timeit("slow_primes(1_000_000_000_000)"			,       setup=UpperCAmelCase__			,       number=1_00_00_00       )       )
 print(timeit("primes(1_000_000_000_000)"			,       setup=UpperCAmelCase__			,       number=1_00_00_00       )       )
 print(timeit("fast_primes(1_000_000_000_000)"			,       setup=UpperCAmelCase__			,       number=1_00_00_00       )       )


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





"""simple docstring"""






import math



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



def 			A__		(					_UpperCAmelCase    :      int = 60_08_51_47_51_43	)							->	int:

	'''simple docstring'''


	try:
		snake_case__  :						List[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__  :						int		=      0
	if is_prime(_UpperCAmelCase	):
		return n
	while n % 2 == 0:
		n //= 2
	if is_prime(_UpperCAmelCase	):
		return n
	for i in range(3				,    int(math.sqrt(_UpperCAmelCase	)	) + 1				,    2	):
		if n % i == 0:
			if is_prime(n // i	):
				snake_case__  :						int		=      n // i
				break
			elif is_prime(_UpperCAmelCase	):
				snake_case__  :						List[Any]		=      i
	return max_number


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





