


import math

def   UpperCamelCase__   (    UpperCAmelCase_			)						->							bool:




       '''simple docstring'''






       if 1 < number < 4:
              # 2 and 3 are primes
              return True
       elif number < 2 or number % 2 == 0 or number % 3 == 0:
              # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
              return False

       # All primes number are in format of 6k +/- 1
       for i in range(5    ,     int(math.sqrt(UpperCAmelCase_			) + 1			)    ,     6			):
              if number % i == 0 or number % (i + 2) == 0:
                     return False
       return True

def   UpperCamelCase__   (    UpperCAmelCase_ = 1000    ,     UpperCAmelCase_ = 1000			)						->							int:




       '''simple docstring'''






       _lowercase					:				str           =			[0, 0, 0]  # length, a, b
       for a in range((a_limit * -1) + 1    ,     UpperCAmelCase_			):
              for b in range(2    ,     UpperCAmelCase_			):
                     if is_prime(UpperCAmelCase_			):
                            _lowercase					:				Any           =			0
                            _lowercase					:				Union[str, Any]           =			0
                            while is_prime((n**2) + (a * n) + b			):
                                   count += 1
                                   n += 1
                            if count > longest[0]:
                                   _lowercase					:				int           =			[count, a, b]
       _lowercase					:				Any           =			longest[1] * longest[2]
       return ans


if __name__ == "__main__":
   print(solution(1_000, 1_000))



from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


UpperCamelCase__				       =			{
    'configuration_wav2vec2_conformer': [
        'WAV2VEC2_CONFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'Wav2Vec2ConformerConfig',
    ],
}


try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCamelCase__				       =			[
       'WAV2VEC2_CONFORMER_PRETRAINED_MODEL_ARCHIVE_LIST',
       'Wav2Vec2ConformerForAudioFrameClassification',
       'Wav2Vec2ConformerForCTC',
       'Wav2Vec2ConformerForPreTraining',
       'Wav2Vec2ConformerForSequenceClassification',
       'Wav2Vec2ConformerForXVector',
       'Wav2Vec2ConformerModel',
       'Wav2Vec2ConformerPreTrainedModel',
   ]

if TYPE_CHECKING:
   from .configuration_wavaveca_conformer import (
       WAV2VEC2_CONFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
       WavaVecaConformerConfig,
   )

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_wavaveca_conformer import (
          WAV2VEC2_CONFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
          WavaVecaConformerForAudioFrameClassification,
          WavaVecaConformerForCTC,
          WavaVecaConformerForPreTraining,
          WavaVecaConformerForSequenceClassification,
          WavaVecaConformerForXVector,
          WavaVecaConformerModel,
          WavaVecaConformerPreTrainedModel,
      )

else:
   import sys

   UpperCamelCase__				       =			_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)