




import math
from collections.abc import Generator




def     __SCREAMING_SNAKE_CASE      (     lowercase_					)				->		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     __SCREAMING_SNAKE_CASE      (     lowercase_					)				->		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     __SCREAMING_SNAKE_CASE      (     lowercase_					)				->		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     __SCREAMING_SNAKE_CASE      (     )				->		List[Any]:

    """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=1_00_00_00					)					)
    print(timeit('''primes(1_000_000_000_000)'''    ,   setup=lowercase_    ,   number=1_00_00_00					)					)
    print(timeit('''fast_primes(1_000_000_000_000)'''    ,   setup=lowercase_    ,   number=1_00_00_00					)					)


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












def     __SCREAMING_SNAKE_CASE      (     lowercase_					)				->		bool:

    """simple docstring"""


    if not isinstance(lowercase_    ,   lowercase_					):
        __UpperCamelCase     						=  F"Input value of [number={number}] must be an integer"
        raise TypeError(lowercase_					)
    if number < 0 or number % 2 == 1:
        return False
    __UpperCamelCase     						=  int(number**0.5					)
    return number == number_sqrt * (number_sqrt + 1)


if __name__ == "__main__":
 import doctest

 doctest.testmod()






