


'''simple docstring'''


import math
from collections.abc import Generator


def 		_lowercase   (SCREAMING_SNAKE_CASE       ):




     '''simple docstring'''





     __A  :					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					,				SCREAMING_SNAKE_CASE       ):
               if (i % j) == 0:
                    break
          else:
               yield i


def 		_lowercase   (SCREAMING_SNAKE_CASE       ):




     '''simple docstring'''





     __A  :					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)
          __A  :					Optional[Any]						     =       int(math.sqrt(SCREAMING_SNAKE_CASE       )       ) + 1
          for j in range(2					,				SCREAMING_SNAKE_CASE       ):
               if (i % j) == 0:
                    break
          else:
               yield i


def 		_lowercase   (SCREAMING_SNAKE_CASE       ):




     '''simple docstring'''





     __A  :					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):
          __A  :					List[str]						     =       int(math.sqrt(SCREAMING_SNAKE_CASE       )       ) + 1
          for j in range(3					,				SCREAMING_SNAKE_CASE					,				2       ):
               # As we removed the even numbers, we don't need them now
               if (i % j) == 0:
                    break
          else:
               yield i


def 		_lowercase   ():




     '''simple docstring'''





     from timeit import timeit

     __A  :					List[str]						     =       "from __main__ import slow_primes, primes, fast_primes"
     print(timeit("slow_primes(1_000_000_000_000)"					,				setup=SCREAMING_SNAKE_CASE					,				number=100_0000       )       )
     print(timeit("primes(1_000_000_000_000)"					,				setup=SCREAMING_SNAKE_CASE					,				number=100_0000       )       )
     print(timeit("fast_primes(1_000_000_000_000)"					,				setup=SCREAMING_SNAKE_CASE					,				number=100_0000       )       )


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





'''simple docstring'''


import math
from collections.abc import Generator


def 		_lowercase   (SCREAMING_SNAKE_CASE       ):




     '''simple docstring'''





     __A  :					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					,				SCREAMING_SNAKE_CASE       ):
               if (i % j) == 0:
                    break
          else:
               yield i


def 		_lowercase   (SCREAMING_SNAKE_CASE       ):




     '''simple docstring'''





     __A  :					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)
          __A  :					Optional[Any]						     =       int(math.sqrt(SCREAMING_SNAKE_CASE       )       ) + 1
          for j in range(2					,				SCREAMING_SNAKE_CASE       ):
               if (i % j) == 0:
                    break
          else:
               yield i


def 		_lowercase   (SCREAMING_SNAKE_CASE       ):




     '''simple docstring'''





     __A  :					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):
          __A  :					List[str]						     =       int(math.sqrt(SCREAMING_SNAKE_CASE       )       ) + 1
          for j in range(3					,				SCREAMING_SNAKE_CASE					,				2       ):
               # As we removed the even numbers, we don't need them now
               if (i % j) == 0:
                    break
          else:
               yield i


def 		_lowercase   ():




     '''simple docstring'''





     from timeit import timeit

     __A  :					List[str]						     =       "from __main__ import slow_primes, primes, fast_primes"
     print(timeit("slow_primes(1_000_000_000_000)"					,				setup=SCREAMING_SNAKE_CASE					,				number=100_0000       )       )
     print(timeit("primes(1_000_000_000_000)"					,				setup=SCREAMING_SNAKE_CASE					,				number=100_0000       )       )
     print(timeit("fast_primes(1_000_000_000_000)"					,				setup=SCREAMING_SNAKE_CASE					,				number=100_0000       )       )


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

