





'''simple docstring'''
import math
from collections.abc import Generator
def     lowercase__       (       __lowercase						:  int					)			->				Generator[int, None, None]:



       """simple docstring"""






       __UpperCamelCase	=  (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     lowercase__       (       __lowercase						:  int					)			->				Generator[int, None, None]:



       """simple docstring"""






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



       """simple docstring"""






       __UpperCamelCase	=  (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	=  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     lowercase__       (       )			->				Tuple:



       """simple docstring"""






       from timeit import timeit

       __UpperCamelCase	=  '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__":
    a__							:							List[str]			=int(input('''Calculate primes up to:\n>> ''').strip())
    for ret in primes(number):
        print(ret)
    benchmark()







'''simple docstring'''
a__							:							int			='''
# Transformers installation
! pip install transformers datasets evaluate
# To install from source instead of the last release, comment the command above and uncomment the following one.
# ! pip install git+https://github.com/huggingface/transformers.git
'''

a__							:							List[Any]			=[{'''type''': '''code''', '''content''': INSTALL_CONTENT}]
a__							:							Dict			={
    '''{processor_class}''': '''FakeProcessorClass''',
    '''{model_class}''': '''FakeModelClass''',
    '''{object_class}''': '''FakeObjectClass''',
}
