"""simple docstring"""







import math



def       A__    (	lowercase_     :	int						)  ->							bool:

   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       A__    (	lowercase_     :	int = 1000      , lowercase_     :	int = 1000						)  ->							int:
   __lowerCamelCase    		=					[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_						):
            __lowerCamelCase    		=					0
            __lowerCamelCase    		=					0
            while is_prime((n**2) + (a * n) + b						):
               count += 1
               n += 1
            if count > longest[0]:
               __lowerCamelCase    		=					[count, a, b]
   __lowerCamelCase    		=					longest[1] * longest[2]
   return ans


if __name__ == "__main__":
     print(solution(1_0_0_0, 1_0_0_0))










'''simple docstring'''

from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available


__lowercase:		Tuple    						=  {
    "configuration_imagegpt": ["IMAGEGPT_PRETRAINED_CONFIG_ARCHIVE_MAP", "ImageGPTConfig", "ImageGPTOnnxConfig"]
}

try:
       if not is_vision_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       __lowercase:		List[str]    						=  ["ImageGPTFeatureExtractor"]
       __lowercase:		Tuple    						=  ["ImageGPTImageProcessor"]

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       __lowercase:		str    						=  [
           "IMAGEGPT_PRETRAINED_MODEL_ARCHIVE_LIST",
           "ImageGPTForCausalImageModeling",
           "ImageGPTForImageClassification",
           "ImageGPTModel",
           "ImageGPTPreTrainedModel",
           "load_tf_weights_in_imagegpt",
       ]


if TYPE_CHECKING:
       from .configuration_imagegpt import IMAGEGPT_PRETRAINED_CONFIG_ARCHIVE_MAP, ImageGPTConfig, ImageGPTOnnxConfig

       try:
              if not is_vision_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .feature_extraction_imagegpt import ImageGPTFeatureExtractor
              from .image_processing_imagegpt import ImageGPTImageProcessor

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_imagegpt import (
                  IMAGEGPT_PRETRAINED_MODEL_ARCHIVE_LIST,
                  ImageGPTForCausalImageModeling,
                  ImageGPTForImageClassification,
                  ImageGPTModel,
                  ImageGPTPreTrainedModel,
                  load_tf_weights_in_imagegpt,
              )

else:
       import sys

       __lowercase:		List[str]    						=  _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)