

'''simple docstring'''
import random







def  _A		(     snake_case					)      ->     bool:
   _lowercase      :				Dict      					=       num - 1
   _lowercase      :				List[str]      					=       0

   while s % 2 == 0:
      _lowercase      :				Any      					=       s // 2
      t += 1

   for _ in range(5					):
      _lowercase      :				List[str]      					=       random.randrange(2		,							num - 1					)
      _lowercase      :				Tuple      					=       pow(snake_case		,							snake_case		,							snake_case					)
      if v != 1:
         _lowercase      :				Any      					=       0
         while v != (num - 1):
            if i == t - 1:
               return False
            else:
               _lowercase      :				List[str]      					=       i + 1
               _lowercase      :				List[str]      					=       (v**2) % num
   return True







def  _A		(     snake_case					)      ->     bool:
   if num < 2:
      return False

   _lowercase      :				Optional[Any]      					=       [
       2,
       3,
       5,
       7,
       11,
       13,
       17,
       19,
       23,
       29,
       31,
       37,
       41,
       43,
       47,
       53,
       59,
       61,
       67,
       71,
       73,
       79,
       83,
       89,
       97,
       1_01,
       1_03,
       1_07,
       1_09,
       1_13,
       1_27,
       1_31,
       1_37,
       1_39,
       1_49,
       1_51,
       1_57,
       1_63,
       1_67,
       1_73,
       1_79,
       1_81,
       1_91,
       1_93,
       1_97,
       1_99,
       2_11,
       2_23,
       2_27,
       2_29,
       2_33,
       2_39,
       2_41,
       2_51,
       2_57,
       2_63,
       2_69,
       2_71,
       2_77,
       2_81,
       2_83,
       2_93,
       3_07,
       3_11,
       3_13,
       3_17,
       3_31,
       3_37,
       3_47,
       3_49,
       3_53,
       3_59,
       3_67,
       3_73,
       3_79,
       3_83,
       3_89,
       3_97,
       4_01,
       4_09,
       4_19,
       4_21,
       4_31,
       4_33,
       4_39,
       4_43,
       4_49,
       4_57,
       4_61,
       4_63,
       4_67,
       4_79,
       4_87,
       4_91,
       4_99,
       5_03,
       5_09,
       5_21,
       5_23,
       5_41,
       5_47,
       5_57,
       5_63,
       5_69,
       5_71,
       5_77,
       5_87,
       5_93,
       5_99,
       6_01,
       6_07,
       6_13,
       6_17,
       6_19,
       6_31,
       6_41,
       6_43,
       6_47,
       6_53,
       6_59,
       6_61,
       6_73,
       6_77,
       6_83,
       6_91,
       7_01,
       7_09,
       7_19,
       7_27,
       7_33,
       7_39,
       7_43,
       7_51,
       7_57,
       7_61,
       7_69,
       7_73,
       7_87,
       7_97,
       8_09,
       8_11,
       8_21,
       8_23,
       8_27,
       8_29,
       8_39,
       8_53,
       8_57,
       8_59,
       8_63,
       8_77,
       8_81,
       8_83,
       8_87,
       9_07,
       9_11,
       9_19,
       9_29,
       9_37,
       9_41,
       9_47,
       9_53,
       9_67,
       9_71,
       9_77,
       9_83,
       9_91,
       9_97,
   ]

   if num in low_primes:
      return True

   for prime in low_primes:
      if (num % prime) == 0:
         return False

   return rabin_miller(snake_case					)







def  _A		(     snake_case = 10_24					)      ->     int:
   while True:
      _lowercase      :				List[Any]      					=       random.randrange(2 ** (keysize - 1)		,							2 ** (keysize)					)
      if is_prime_low_num(snake_case					):
         return num


if __name__ == "__main__":
    _snake_case         =  generate_large_prime()
    print(('Prime number:', num))
    print(('is_prime_low_num:', is_prime_low_num(num)))









'''simple docstring'''
from sklearn.metrics import mean_squared_error

import datasets


_snake_case         =  '\\n@article{scikit-learn,\n title={Scikit-learn: Machine Learning in {P}ython},\n author={Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V.\n         and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P.\n         and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and\n         Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.},\n journal={Journal of Machine Learning Research},\n volume={12},\n pages={2825--2830},\n year={2011}\n}\n'

_snake_case         =  '\\nMean Squared Error(MSE) is the average of the square of difference between the predicted\nand actual values.\n'


_snake_case         =  '\nArgs:\n    predictions: array-like of shape (n_samples,) or (n_samples, n_outputs)\n        Estimated target values.\n    references: array-like of shape (n_samples,) or (n_samples, n_outputs)\n        Ground truth (correct) target values.\n    sample_weight: array-like of shape (n_samples,), default=None\n        Sample weights.\n    multioutput: {"raw_values", "uniform_average"} or array-like of shape (n_outputs,), default="uniform_average"\n        Defines aggregating of multiple output values. Array-like value defines weights used to average errors.\n\n        "raw_values" : Returns a full set of errors in case of multioutput input.\n\n        "uniform_average" : Errors of all outputs are averaged with uniform weight.\n\n    squared : bool, default=True\n        If True returns MSE value, if False returns RMSE (Root Mean Squared Error) value.\n\nReturns:\n    mse : mean squared error.\nExamples:\n\n    >>> mse_metric = datasets.load_metric("mse")\n    >>> predictions = [2.5, 0.0, 2, 8]\n    >>> references = [3, -0.5, 2, 7]\n    >>> results = mse_metric.compute(predictions=predictions, references=references)\n    >>> print(results)\n    {\'mse\': 0.375}\n    >>> rmse_result = mse_metric.compute(predictions=predictions, references=references, squared=False)\n    >>> print(rmse_result)\n    {\'mse\': 0.6123724356957945}\n\n    If you\'re using multi-dimensional lists, then set the config as follows :\n\n    >>> mse_metric = datasets.load_metric("mse", "multilist")\n    >>> predictions = [[0.5, 1], [-1, 1], [7, -6]]\n    >>> references = [[0, 2], [-1, 2], [8, -5]]\n    >>> results = mse_metric.compute(predictions=predictions, references=references)\n    >>> print(results)\n    {\'mse\': 0.7083333333333334}\n    >>> results = mse_metric.compute(predictions=predictions, references=references, multioutput=\'raw_values\')\n    >>> print(results) # doctest: +NORMALIZE_WHITESPACE\n    {\'mse\': array([0.41666667, 1. ])}\n'


@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION  ,				_KWARGS_DESCRIPTION  )
class        a__  (							datasets.Metric  ):


   def 						_lowerCamelCase       (			self  ):





      """simple docstring"""





      return datasets.MetricInfo(
          description=_DESCRIPTION      ,    citation=_CITATION      ,    inputs_description=_KWARGS_DESCRIPTION      ,    features=datasets.Features(self._get_feature_types()  )      ,    reference_urls=[
              "https://scikit-learn.org/stable/modules/generated/sklearn.metrics.mean_squared_error.html"
          ]      ,    )


   def 						_lowerCamelCase       (			self  ):





      """simple docstring"""





      if self.config_name == "multilist":
         return {
             "predictions": datasets.Sequence(datasets.Value("float"  )  ),
             "references": datasets.Sequence(datasets.Value("float"  )  ),
         }
      else:
         return {
             "predictions": datasets.Value("float"  ),
             "references": datasets.Value("float"  ),
         }






   def 						_lowerCamelCase       (			self      ,    _UpperCamelCase      ,    _UpperCamelCase      ,    _UpperCamelCase=None      ,    _UpperCamelCase="uniform_average"      ,    _UpperCamelCase=True  ):





      """simple docstring"""





      _lowercase      :				str      					=       mean_squared_error(
          _UpperCamelCase      ,    _UpperCamelCase      ,    sample_weight=_UpperCamelCase      ,    multioutput=_UpperCamelCase      ,    squared=_UpperCamelCase  )

      return {"mse": mse}






