def A__  (			lowercase:     int					)				->		bool:

       if p < 2:
              raise ValueError('p should not be less than 2!'					)
       elif p == 2:
              return True

       A						:     int         =4
       A						:     List[Any]         =(1 << p) - 1
       for _ in range(p - 2					):
              A						:     Optional[int]         =((s * s) - 2) % m
       return s == 0


if __name__ == "__main__":
    print(lucas_lehmer_test(7))
    print(lucas_lehmer_test(1_1))







import logging
from dataclasses import dataclass, field
from typing import Optional

from seqaseq_trainer import arg_to_scheduler

from transformers import TrainingArguments


_lowercase							:      Any      							=logging.getLogger(__name__)



@dataclass
class  SCREAMING_SNAKE_CASE_ (					lowerCAmelCase_			):
  '''simple docstring'''


  lowercase		:     Optional[float]            =				field(
      default=0.0   ,						metadata={"help": "The label smoothing epsilon to apply (if not zero)."}			)
  lowercase		:     bool            =				field(default=lowerCAmelCase_   ,						metadata={"help": "Whether to SortishSamler or not."}			)
  lowercase		:     bool            =				field(
      default=lowerCAmelCase_   ,						metadata={"help": "Whether to use generate to calculate generative metrics (ROUGE, BLEU)."}			)
  lowercase		:     bool            =				field(default=lowerCAmelCase_   ,						metadata={"help": "whether to use adafactor"}			)
  lowercase		:     Optional[float]            =				field(
      default=lowerCAmelCase_   ,						metadata={"help": "Encoder layer dropout probability. Goes into model.config."}			)
  lowercase		:     Optional[float]            =				field(
      default=lowerCAmelCase_   ,						metadata={"help": "Decoder layer dropout probability. Goes into model.config."}			)
  lowercase		:     Optional[float]            =				field(default=lowerCAmelCase_   ,						metadata={"help": "Dropout probability. Goes into model.config."}			)
  lowercase		:     Optional[float]            =				field(
      default=lowerCAmelCase_   ,						metadata={"help": "Attention dropout probability. Goes into model.config."}			)
  lowercase		:     Optional[str]            =				field(
      default="linear"   ,						metadata={"help": f'Which lr scheduler to use. Selected in {sorted(arg_to_scheduler.keys()			)}'}   ,						)






