
"""simple docstring"""





import math
from collections.abc import Generator







def       __a	(						__lowerCamelCase    ):
   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,						__lowerCamelCase    ):
         if (i % j) == 0:
            break
      else:
         yield i







def       __a	(						__lowerCamelCase    ):
   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_   :   Optional[int]     	=       int(math.sqrt(__lowerCamelCase    )    ) + 1
      for j in range(2,						__lowerCamelCase    ):
         if (i % j) == 0:
            break
      else:
         yield i







def       __a	(						__lowerCamelCase    ):
   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_   :   Any     	=       int(math.sqrt(__lowerCamelCase    )    ) + 1
      for j in range(3,						__lowerCamelCase,						2    ):
         # As we removed the even numbers, we don't need them now
         if (i % j) == 0:
            break
      else:
         yield i







def       __a	(						):
   from timeit import timeit

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


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



import math
def 					__lowercase						(    lowerCamelCase__       )					->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(lowerCamelCase__       ) + 1       )			,					6       ):
    if number % i == 0 or number % (i + 2) == 0:
      return False
  return True
def 					__lowercase						(    lowerCamelCase__ = 2_00_00_00       )					->int:

  '''simple docstring'''




  return sum(num for num in range(3			,					lowerCamelCase__			,					2       ) if is_prime(lowerCamelCase__       )       ) + 2 if n > 2 else 0


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

