

from math import isqrt, loga







def 						lowerCamelCase__      ( __A    :int		):


       """simple docstring"""




       __snake_case       	=							[True] * max_number
       for i in range(2	,isqrt(max_number - 1		) + 1		):
              if is_prime[i]:
                     for j in range(i**2	,__A	,__A		):
                            __snake_case       	=							False

       return [i for i in range(2	,__A		) if is_prime[i]]







def 						lowerCamelCase__      ( __A    :int = 8_0_0_8_0_0	,__A    :int = 8_0_0_8_0_0		):


       """simple docstring"""




       __snake_case       	=							degree * loga(__A		)
       __snake_case       	=							int(__A		)
       __snake_case       	=							calculate_prime_numbers(__A		)

       __snake_case       	=							0
       __snake_case       	=							0
       __snake_case       	=							len(__A		) - 1
       while left < right:
              while (
                  prime_numbers[right] * loga(prime_numbers[left]		)
                  + prime_numbers[left] * loga(prime_numbers[right]		)
                  > upper_bound
              ):
                     right -= 1
              hybrid_integers_count += right - left
              left += 1

       return hybrid_integers_count


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




def 						lowerCamelCase__      ( __A    :int	,__A    :float	,__A    :float		):


       """simple docstring"""




       return round(float(moles / volume		) * nfactor		)







def 						lowerCamelCase__      ( __A    :float	,__A    :float	,__A    :float		):


       """simple docstring"""




       return round(float((moles * 0.0_821 * temperature) / (volume)		)		)







def 						lowerCamelCase__      ( __A    :float	,__A    :float	,__A    :float		):


       """simple docstring"""




       return round(float((moles * 0.0_821 * temperature) / (pressure)		)		)







def 						lowerCamelCase__      ( __A    :float	,__A    :float	,__A    :float		):


       """simple docstring"""




       return round(float((pressure * volume) / (0.0_821 * moles)		)		)


if __name__ == "__main__":
    import doctest

    doctest.testmod()

