
"""simple docstring"""



import math






def       lowerCamelCase					(a_						:int)     ->							List[str]:
       lowercase		:Tuple       							=				[]
       lowercase		:Optional[Any]       							=				2
       lowercase		:Optional[int]       							=				int(math.sqrt(lowerCAmelCase__))  # Size of every segment
       lowercase		:Optional[int]       							=				[True] * (end + 1)
       lowercase		:str       							=				[]

       while start <= end:
              if temp[start] is True:
                     in_prime.append(lowerCAmelCase__)
                     for i in range(start * start				,				end + 1				,				lowerCAmelCase__):
                            lowercase		:Union[str, Any]       							=				False
              start += 1
       prime += in_prime

       lowercase		:List[Any]       							=				end + 1
       lowercase		:Union[str, Any]       							=				min(2 * end				,				lowerCAmelCase__)

       while low <= n:
              lowercase		:Union[str, Any]       							=				[True] * (high - low + 1)
              for each in in_prime:
                     lowercase		:Optional[int]       							=				math.floor(low / each) * each
                     if t < low:
                            t += each

                     for j in range(lowerCAmelCase__				,				high + 1				,				lowerCAmelCase__):
                            lowercase		:Optional[Any]       							=				False

              for j in range(len(lowerCAmelCase__)):
                     if temp[j] is True:
                            prime.append(j + low)

              lowercase		:str       							=				high + 1
              lowercase		:Dict       							=				min(high + end				,				lowerCAmelCase__)

       return prime




print(sieve(10**6))





"""simple docstring"""



import math






def       lowerCamelCase					(a_						:int)     ->							bool:
       assert isinstance(a_				,				a_) and (
           number >= 0
       ), "'number' must been an int and positive"

       if 1 < number < 4:
              # 2 and 3 are primes
              return True
       elif number < 2 or not number % 2:
              # Negatives, 0, 1 and all even numbers are not primes
              return False

       lowercase		:Any       							=				range(3				,				int(math.sqrt(a_) + 1)				,				2)
       return not any(not number % i for i in odd_numbers)






def       lowerCamelCase					(a_						:Optional[int]				,				a_						:Optional[int]=1				,				**a_						:List[str])     ->							Any:
       lowercase		:str       							=				factor * value
       lowercase		:int       							=				value

       while not is_prime(a_):
              value += 1 if not ("desc" in kwargs and kwargs["desc"] is True) else -1

       if value == first_value_val:
              return next_prime(value + 1				,				**a_)
       return value

