


"""simple docstring"""







import random

from .binary_exp_mod import bin_exp_mod
def 					a__			(				SCREAMING_SNAKE_CASE    :    Optional[Any]				,      SCREAMING_SNAKE_CASE    :    List[Any]=1_0_0_0				):


  '''simple docstring'''







  if n < 2:
    return False

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

  # this means n is odd
  lowerCAmelCase     :     Optional[Any]								=							n - 1
  lowerCAmelCase     :     Optional[Any]								=							0
  while d % 2 == 0:
    d /= 2
    exp += 1

  # n - 1=d*(2**exp)
  lowerCAmelCase     :     Optional[Any]								=							0
  while count < prec:
    lowerCAmelCase     :     Optional[int]								=							random.randint(2				,      n - 1				)
    lowerCAmelCase     :     str								=							bin_exp_mod(_lowerCamelCase				,      _lowerCamelCase				,      _lowerCamelCase				)
    if b != 1:
      lowerCAmelCase     :     Optional[int]								=							True
      for _ in range(_lowerCamelCase				):
        if b == n - 1:
          lowerCAmelCase     :     List[Any]								=							False
          break
        lowerCAmelCase     :     int								=							b * b
        b %= n
      if flag:
        return False
      count += 1
  return True


if __name__ == "__main__":
     lowerCAmelCase__      				=   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"""





from math import pow, sqrt







def      lowerCamelCase__       (							*_lowerCamelCase       :		float )      ->				bool:
  lowerCamelCase_         =						len(_lowerCamelCase ) > 0 and all(value > 0.0 for value in values )
  return result







def      lowerCamelCase__       (							_lowerCamelCase       :		float		,				_lowerCamelCase       :		float )      ->				float | ValueError:
  return (
      round(sqrt(molar_mass_a / molar_mass_a )		,				6 )
      if validate(_lowerCamelCase		,				_lowerCamelCase )
      else ValueError('Input Error: Molar mass values must greater than 0.' )
  )







def      lowerCamelCase__       (							_lowerCamelCase       :		float		,				_lowerCamelCase       :		float		,				_lowerCamelCase       :		float )      ->				float | ValueError:
  return (
      round(effusion_rate * sqrt(molar_mass_a / molar_mass_a )		,				6 )
      if validate(_lowerCamelCase		,				_lowerCamelCase		,				_lowerCamelCase )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.' )
  )







def      lowerCamelCase__       (							_lowerCamelCase       :		float		,				_lowerCamelCase       :		float		,				_lowerCamelCase       :		float )      ->				float | ValueError:
  return (
      round(effusion_rate / sqrt(molar_mass_a / molar_mass_a )		,				6 )
      if validate(_lowerCamelCase		,				_lowerCamelCase		,				_lowerCamelCase )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.' )
  )







def      lowerCamelCase__       (							_lowerCamelCase       :		float		,				_lowerCamelCase       :		float		,				_lowerCamelCase       :		float )      ->				float | ValueError:
  return (
      round(molar_mass / pow(effusion_rate_a / effusion_rate_a		,				2 )		,				6 )
      if validate(_lowerCamelCase		,				_lowerCamelCase		,				_lowerCamelCase )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.' )
  )







def      lowerCamelCase__       (							_lowerCamelCase       :		float		,				_lowerCamelCase       :		float		,				_lowerCamelCase       :		float )      ->				float | ValueError:
  return (
      round(pow(effusion_rate_a / effusion_rate_a		,				2 ) / molar_mass		,				6 )
      if validate(_lowerCamelCase		,				_lowerCamelCase		,				_lowerCamelCase )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.' )
  )




