
"""simple docstring"""
import math
from collections.abc import Generator
def 					a__ ( a :					int		):

  """simple docstring"""







  _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							,  a		):
      if (i % j) == 0:
        break
    else:
      yield i
def 					a__ ( a :					int		):

  """simple docstring"""







  _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)
    _snake_case  :    List[Any]            = int(math.sqrt(a		)		) + 1
    for j in range(2							,  a		):
      if (i % j) == 0:
        break
    else:
      yield i
def 					a__ ( a :					int		):

  """simple docstring"""







  _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):
    _snake_case  :    List[str]            = 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 					a__ ( ):

  """simple docstring"""







  from timeit import timeit

  _snake_case  :    str            = "from __main__ import slow_primes, primes, fast_primes"
  print(timeit("slow_primes(1_000_000_000_000)"							,  setup=a							,  number=1_000_000		)		)
  print(timeit("primes(1_000_000_000_000)"							,  setup=a							,  number=1_000_000		)		)
  print(timeit("fast_primes(1_000_000_000_000)"							,  setup=a							,  number=1_000_000		)		)


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





'''simple docstring'''







from __future__ import annotations

from enum import Enum, unique
from typing import TypeVar

# Create a generic variable that can be 'Enum', or any subclass.
a__    :   Optional[Any]								=			TypeVar('T', bound='Enum')
@unique
class    lowercase_	(       a__  ):
    __UpperCAmelCase       =      80
    __UpperCAmelCase       =      70
    __UpperCAmelCase       =      60
    __UpperCAmelCase       =      50
    __UpperCAmelCase       =      40
    __UpperCAmelCase       =      30
    __UpperCAmelCase       =      20
    __UpperCAmelCase       =      10

@unique
class    lowercase_	(       a__  ):
    __UpperCAmelCase       =      24
    __UpperCAmelCase       =      21
    __UpperCAmelCase       =      18
    __UpperCAmelCase       =      15
    __UpperCAmelCase       =      12
    __UpperCAmelCase       =      9
    __UpperCAmelCase       =      6
    __UpperCAmelCase       =      3
    __UpperCAmelCase       =      2
    __UpperCAmelCase       =      1
    __UpperCAmelCase       =      -1
    __UpperCAmelCase       =      -2
    __UpperCAmelCase       =      -3
    __UpperCAmelCase       =      -6
    __UpperCAmelCase       =      -9
    __UpperCAmelCase       =      -12
    __UpperCAmelCase       =      -15
    __UpperCAmelCase       =      -18
    __UpperCAmelCase       =      -21
    __UpperCAmelCase       =      -24


    @classmethod
    def   __a				(	cls       ):
          return {unit.name: unit.value for unit in cls if unit.value > 0}


    @classmethod
    def   __a				(	cls       ):
          return {unit.name: unit.value for unit in cls if unit.value < 0}







def _UpperCamelCase			(	__A       )				->						str:


      '''simple docstring'''



      UpperCamelCase__      =							SIUnit.get_positive() if value > 0 else SIUnit.get_negative()
      for name_prefix, value_prefix in prefixes.items():
            UpperCamelCase__      =							value / (10**value_prefix)
            if numerical_part > 1:
                  return F'''{numerical_part!s} {name_prefix}'''
      return str(__A       )







def _UpperCamelCase			(	__A       )				->						str:


      '''simple docstring'''



      for prefix in BinaryUnit:
            UpperCamelCase__      =							value / (2**prefix.value)
            if numerical_part > 1:
                  return F'''{numerical_part!s} {prefix.name}'''
      return str(__A       )


if __name__ == "__main__":
  import doctest

  doctest.testmod()





