






def      lowerCamelCase__	(   lowercase  ,   lowercase ):

  """simple docstring"""






  SCREAMING_SNAKE_CASE				:					Any		  =			(boundary[1] - boundary[0]) / steps
  SCREAMING_SNAKE_CASE				:					Optional[int]		  =			boundary[0]
  SCREAMING_SNAKE_CASE				:					Tuple		  =			boundary[1]
  SCREAMING_SNAKE_CASE				:					Union[str, Any]		  =			make_points(lowercase  ,   lowercase  ,   lowercase )
  SCREAMING_SNAKE_CASE				:					List[Any]		  =			0.0
  y += (h / 3.0) * f(lowercase )
  SCREAMING_SNAKE_CASE				:					List[str]		  =			2
  for i in x_i:
    y += (h / 3) * (4 - 2 * (cnt % 2)) * f(lowercase )
    cnt += 1
  y += (h / 3.0) * f(lowercase )
  return y


def      lowerCamelCase__	(   lowercase  ,   lowercase  ,   lowercase ):

  """simple docstring"""






  SCREAMING_SNAKE_CASE				:					Dict		  =			a + h
  while x < (b - h):
    yield x
    SCREAMING_SNAKE_CASE				:					List[str]		  =			x + h


def      lowerCamelCase__	(   lowercase ):  # enter your function here

  """simple docstring"""






  SCREAMING_SNAKE_CASE				:					Dict		  =			(x - 0) * (x - 0)
  return y


def      lowerCamelCase__	(   ):

  """simple docstring"""






  SCREAMING_SNAKE_CASE				:					Optional[int]		  =			0.0  # Lower bound of integration
  SCREAMING_SNAKE_CASE				:					str		  =			1.0  # Upper bound of integration
  SCREAMING_SNAKE_CASE				:					Optional[Any]		  =			10.0  # define number of steps or resolution
  SCREAMING_SNAKE_CASE				:					Tuple		  =			[a, b]  # define boundary of integration
  SCREAMING_SNAKE_CASE				:					Optional[Any]		  =			method_a(lowercase  ,   lowercase )
  print(F'''y = {y}''' )


if __name__ == "__main__":
   main()














import math
from collections.abc import Generator


def      lowerCamelCase__	(   lowercase ):

  """simple docstring"""






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


def      lowerCamelCase__	(   lowercase ):

  """simple docstring"""






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


def      lowerCamelCase__	(   lowercase ):

  """simple docstring"""






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


def      lowerCamelCase__	(   ):

  """simple docstring"""






  from timeit import timeit

  SCREAMING_SNAKE_CASE				:					Tuple		  =			"from __main__ import slow_primes, primes, fast_primes"
  print(timeit("slow_primes(1_000_000_000_000)"  ,   setup=lowercase  ,   number=1000000 ) )
  print(timeit("primes(1_000_000_000_000)"  ,   setup=lowercase  ,   number=1000000 ) )
  print(timeit("fast_primes(1_000_000_000_000)"  ,   setup=lowercase  ,   number=1000000 ) )


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






