


'''simple docstring'''







from itertools import compress, repeat
from math import ceil, sqrt






def       lowerCAmelCase__       (				lowerCamelCase     :			int   ):

       if num <= 2:
              return []
       if num == 3:
              return [2]

       # Odd sieve for numbers in range [3, num - 1]
       _A     :	str      =					bytearray(b'\x01'   ) * ((num >> 1) - 1)

       for i in range(3  ,int(sqrt(lowerCamelCase   )   ) + 1  ,2   ):
              if sieve[(i >> 1) - 1]:
                     _A     :	List[Any]      =					i**2
                     _A     :	Union[str, Any]      =					repeat(
                         0  ,ceil((num - i_squared) / (i << 1)   )   )

       return [2] + list(compress(range(3  ,lowerCamelCase  ,2   )  ,lowerCamelCase   )   )


if __name__ == "__main__":
   import doctest

   doctest.testmod()










'''simple docstring'''







import math






def       lowerCAmelCase__       (				lowerCamelCase     :			int   ):
       _A     :	int      =					math.log(2  ,10   ) * number
       _A     :	List[Any]      =					round((log_number - int(lowerCamelCase   ))  ,15   )

       return difference






def       lowerCAmelCase__       (				lowerCamelCase     :			int = 678910   ):
       _A     :	List[str]      =					90
       _A     :	List[Any]      =					0

       _A     :	List[str]      =					math.log(1.23  ,10   )
       _A     :	Any      =					math.log(1.24  ,10   )
       _A     :	Union[str, Any]      =					0

       while position < number:
              _A     :	Dict      =					log_difference(lowerCamelCase   )

              if difference >= upper_limit:
                     power_iterator += 93

              elif difference < lower_limit:
                     power_iterator += 196

              else:
                     _A     :	str      =					power_iterator
                     power_iterator += 196
                     position += 1

       return previous_power


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   print(f"""{solution() = }""")






