import math
from collections.abc import Generator

def   a_					(_lowerCAmelCase  :   int       )->				Generator[int, None, None]:
    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			,	_lowerCAmelCase       ):
            if (i % j) == 0:
                break
        else:
            yield i

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

def   a_					(_lowerCAmelCase  :   int       )->				Generator[int, None, None]:
    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(_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_					()->				Dict:
    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=_lowerCAmelCase			,	number=1000000       )       )
    print(timeit("""primes(1_000_000_000_000)"""			,	setup=_lowerCAmelCase			,	number=1000000       )       )
    print(timeit("""fast_primes(1_000_000_000_000)"""			,	setup=_lowerCAmelCase			,	number=1000000       )       )


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



def   a_					(_lowerCAmelCase  :   str       )->				int:
    snake_case:						List[str]         =   0
    for letter in data:
        snake_case:						int         =   (hash_ << 4) + ord(_lowerCAmelCase       )
        snake_case:						Optional[int]         =   hash_ & 0xf_0_0_0_0_0_0_0
        if x != 0:
            hash_ ^= x >> 24
        hash_ &= ~x
    return hash_


if __name__ == "__main__":
    import doctest

    doctest.testmod()


