

import math
from collections.abc import Generator





def 	snake_case_      (__A     :						int     )			->	Generator[int, None, None]:
   __lowerCAmelCase  :			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					,   __A     ):
         if (i % j) == 0:
            break
      else:
         yield i





def 	snake_case_      (__A     :						int     )			->	Generator[int, None, None]:
   __lowerCAmelCase  :			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)
      __lowerCAmelCase  :			Dict					    =						int(math.sqrt(__A     )     ) + 1
      for j in range(2					,   __A     ):
         if (i % j) == 0:
            break
      else:
         yield i





def 	snake_case_      (__A     :						int     )			->	Generator[int, None, None]:
   __lowerCAmelCase  :			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):
      __lowerCAmelCase  :			Dict					    =						int(math.sqrt(__A     )     ) + 1
      for j in range(3					,   __A					,   2     ):
         # As we removed the even numbers, we don't need them now
         if (i % j) == 0:
            break
      else:
         yield i





def 	snake_case_      ()			->	Any:
   from timeit import timeit

   __lowerCAmelCase  :			Optional[Any]					    =						"""from __main__ import slow_primes, primes, fast_primes"""
   print(timeit("""slow_primes(1_000_000_000_000)"""					,   setup=__A					,   number=1_0_0_0_0_0_0     )     )
   print(timeit("""primes(1_000_000_000_000)"""					,   setup=__A					,   number=1_0_0_0_0_0_0     )     )
   print(timeit("""fast_primes(1_000_000_000_000)"""					,   setup=__A					,   number=1_0_0_0_0_0_0     )     )


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








def 					SCREAMING_SNAKE_CASE	(       __UpperCamelCase			:						float       ,     __UpperCamelCase			:						float      )  ->							float:
    return a + b


if __name__ == "__main__":
 _lowerCamelCase			 =						5
 _lowerCamelCase			 =						6
 print(F"The sum of {a} + {b} is {add(a, b)}")





