






import random

from .binary_exp_mod import bin_exp_mod







def       lowercase__	(					A_:						List[str]  ,      A_:						Optional[Any]=1000		)	->				List[str]:







       """simple docstring"""






       if n < 2:
              return False

       if n % 2 == 0:
              return n == 2

       # this means n is odd
       __UpperCAmelCase     				=n - 1
       __UpperCAmelCase     				=0
       while d % 2 == 0:
              d /= 2
              exp += 1

       # n - 1=d*(2**exp)
       __UpperCAmelCase     				=0
       while count < prec:
              __UpperCAmelCase     				=random.randint(2  ,      n - 1		)
              __UpperCAmelCase     				=bin_exp_mod(A_  ,      A_  ,      A_		)
              if b != 1:
                     __UpperCAmelCase     				=True
                     for _ in range(A_		):
                            if b == n - 1:
                                   __UpperCAmelCase     				=False
                                   break
                            __UpperCAmelCase     				=b * b
                            b %= n
                     if flag:
                            return False
                     count += 1
       return True


if __name__ == "__main__":
   __A					=	abs(int(input("Enter bound : ").strip()))
   print("Here's the list of primes:")
   print(", ".join(str(i) for i in range(n + 1) if is_prime_big(i)))











"""simple docstring"""



def 						__lowercase	(  snake_case_    :    int = 2000000		)  ->int:



    '''simple docstring'''







    __A       :		List[Any]							=	[0 for i in range(n + 1		)]
    __A       :		str							=	1
    __A       :		Dict							=	1

    for i in range(2							,int(n**0.5		) + 1		):
        if primality_list[i] == 0:
            for j in range(i * i							,n + 1							,snake_case_		):
                __A       :		List[Any]							=	1
    __A       :		Union[str, Any]							=	0
    for i in range(snake_case_		):
        if primality_list[i] == 0:
            sum_of_primes += i
    return sum_of_primes


if __name__ == "__main__":
       print(f'''{solution() = }''')




