
"""simple docstring"""






from __future__ import annotations

from collections.abc import Generator






def 						_snake_case       (	)  ->				Generator[int, None, None]:


			'''simple docstring'''





			lowerCAmelCase_    :dict[int, int]			     =  {}
			lowerCAmelCase_    :int			     =  2
			while True:
						lowerCAmelCase_    :List[Any]			     =  factor_map.pop(lowercase__      ,     lowercase__		)
						if factor:
									lowerCAmelCase_    :Optional[int]			     =  factor + prime
									while x in factor_map:
												x += factor
									lowerCAmelCase_    :List[str]			     =  factor
						else:
									lowerCAmelCase_    :Optional[int]			     =  prime
									yield prime
						prime += 1






def 						_snake_case       (	lowercase__		:  float = 1E10		)  ->				int:


			'''simple docstring'''





			lowerCAmelCase_    :Optional[Any]			     =  sieve()

			lowerCAmelCase_    :str			     =  1
			while True:
						lowerCAmelCase_    :int			     =  next(lowercase__		)
						if (2 * prime * n) > limit:
									return n
						# Ignore the next prime as the reminder will be 2.
						next(lowercase__		)
						n += 2


if __name__ == "__main__":
				print(solution())










# flake8: noqa
# Lint as: python3
UpperCAmelCase__   	=							[
    '''VerificationMode''',
    '''Version''',
    '''disable_progress_bar''',
    '''enable_progress_bar''',
    '''is_progress_bar_enabled''',
    '''experimental''',
]

from .info_utils import VerificationMode
from .logging import disable_progress_bar, enable_progress_bar, is_progress_bar_enabled
from .version import Version
from .experimental import experimental

