




'''simple docstring'''


import math



def    _SCREAMING_SNAKE_CASE    (			UpperCamelCase__						:				Union[str, Any]							):




     """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(lowercase__							) + 1							)   ,						6							):
          if number % i == 0 or number % (i + 2) == 0:
               return False
     return True



def    _SCREAMING_SNAKE_CASE    (			UpperCamelCase__						:				Any = 1000   ,						UpperCamelCase__						:				Dict = 1000							):




     """simple docstring"""


     a_    :       Optional[int]    	=     [0, 0, 0]  # length, a, b
     for a in range((a_limit * -1) + 1   ,						lowercase__							):
          for b in range(2   ,						lowercase__							):
               if is_prime(lowercase__							):
                    a_    :       Tuple    	=     0
                    a_    :       Dict    	=     0
                    while is_prime((n**2) + (a * n) + b							):
                         count += 1
                         n += 1
                    if count > longest[0]:
                         a_    :       str    	=     [count, a, b]
     a_    :       Dict    	=     longest[1] * longest[2]
     return ans


if __name__ == "__main__":
    print(solution(1000, 1000))






'''simple docstring'''


from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


lowerCAmelCase_			:     int							    =     {
    'configuration_dpr': ['DPR_PRETRAINED_CONFIG_ARCHIVE_MAP', 'DPRConfig'],
    'tokenization_dpr': [
        'DPRContextEncoderTokenizer',
        'DPRQuestionEncoderTokenizer',
        'DPRReaderOutput',
        'DPRReaderTokenizer',
    ],
}


try:
 if not is_tokenizers_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 lowerCAmelCase_			:     Union[str, Any]							    =     [
     'DPRContextEncoderTokenizerFast',
     'DPRQuestionEncoderTokenizerFast',
     'DPRReaderTokenizerFast',
 ]

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 lowerCAmelCase_			:     List[str]							    =     [
     'DPR_CONTEXT_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST',
     'DPR_QUESTION_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST',
     'DPR_READER_PRETRAINED_MODEL_ARCHIVE_LIST',
     'DPRContextEncoder',
     'DPRPretrainedContextEncoder',
     'DPRPreTrainedModel',
     'DPRPretrainedQuestionEncoder',
     'DPRPretrainedReader',
     'DPRQuestionEncoder',
     'DPRReader',
 ]

try:
 if not is_tf_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 lowerCAmelCase_			:     Dict							    =     [
     'TF_DPR_CONTEXT_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST',
     'TF_DPR_QUESTION_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST',
     'TF_DPR_READER_PRETRAINED_MODEL_ARCHIVE_LIST',
     'TFDPRContextEncoder',
     'TFDPRPretrainedContextEncoder',
     'TFDPRPretrainedQuestionEncoder',
     'TFDPRPretrainedReader',
     'TFDPRQuestionEncoder',
     'TFDPRReader',
 ]


if TYPE_CHECKING:
 from .configuration_dpr import DPR_PRETRAINED_CONFIG_ARCHIVE_MAP, DPRConfig
 from .tokenization_dpr import (
     DPRContextEncoderTokenizer,
     DPRQuestionEncoderTokenizer,
     DPRReaderOutput,
     DPRReaderTokenizer,
 )

 try:
  if not is_tokenizers_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .tokenization_dpr_fast import (
      DPRContextEncoderTokenizerFast,
      DPRQuestionEncoderTokenizerFast,
      DPRReaderTokenizerFast,
  )

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_dpr import (
      DPR_CONTEXT_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST,
      DPR_QUESTION_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST,
      DPR_READER_PRETRAINED_MODEL_ARCHIVE_LIST,
      DPRContextEncoder,
      DPRPretrainedContextEncoder,
      DPRPreTrainedModel,
      DPRPretrainedQuestionEncoder,
      DPRPretrainedReader,
      DPRQuestionEncoder,
      DPRReader,
  )

 try:
  if not is_tf_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_tf_dpr import (
      TF_DPR_CONTEXT_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST,
      TF_DPR_QUESTION_ENCODER_PRETRAINED_MODEL_ARCHIVE_LIST,
      TF_DPR_READER_PRETRAINED_MODEL_ARCHIVE_LIST,
      TFDPRContextEncoder,
      TFDPRPretrainedContextEncoder,
      TFDPRPretrainedQuestionEncoder,
      TFDPRPretrainedReader,
      TFDPRQuestionEncoder,
      TFDPRReader,
  )

else:
 import sys

 lowerCAmelCase_			:     int							    =     _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)
