



import math
def 						snake_case__							(       __lowercase							)		->		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(__SCREAMING_SNAKE_CASE							) + 1							)				,  6							):
												if number % i == 0 or number % (i + 2) == 0:
																		return False
						return True
def 						snake_case__							(       __lowercase = 1_0_0_0				,  __lowercase = 1_0_0_0							)		->		int:







						"""simple docstring"""

						A__						:				List[Any]         =			[0, 0, 0]  # length, a, b
						for a in range((a_limit * -1) + 1				,  __SCREAMING_SNAKE_CASE							):
												for b in range(2				,  __SCREAMING_SNAKE_CASE							):
																		if is_prime(__SCREAMING_SNAKE_CASE							):
																								A__						:				int         =			0
																								A__						:				List[str]         =			0
																								while is_prime((n**2) + (a * n) + b							):
																														count += 1
																														n += 1
																								if count > longest[0]:
																														A__						:				Dict         =			[count, a, b]
						A__						:				Union[str, Any]         =			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_flax_available,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


A__ :		str					={'configuration_t5': ['T5_PRETRAINED_CONFIG_ARCHIVE_MAP', 'T5Config', 'T5OnnxConfig']}

try:
     if not is_sentencepiece_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     A__ :		Optional[int]					=['T5Tokenizer']

try:
     if not is_tokenizers_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     A__ :		Union[str, Any]					=['T5TokenizerFast']

try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     A__ :		Union[str, Any]					=[
         'T5_PRETRAINED_MODEL_ARCHIVE_LIST',
         'T5EncoderModel',
         'T5ForConditionalGeneration',
         'T5Model',
         'T5PreTrainedModel',
         'load_tf_weights_in_t5',
         'T5ForQuestionAnswering',
     ]

try:
     if not is_tf_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     A__ :		List[str]					=[
         'TF_T5_PRETRAINED_MODEL_ARCHIVE_LIST',
         'TFT5EncoderModel',
         'TFT5ForConditionalGeneration',
         'TFT5Model',
         'TFT5PreTrainedModel',
     ]

try:
     if not is_flax_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     A__ :		Union[str, Any]					=[
         'FlaxT5EncoderModel',
         'FlaxT5ForConditionalGeneration',
         'FlaxT5Model',
         'FlaxT5PreTrainedModel',
     ]


if TYPE_CHECKING:
     from .configuration_ta import T5_PRETRAINED_CONFIG_ARCHIVE_MAP, TaConfig, TaOnnxConfig

     try:
          if not is_sentencepiece_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .tokenization_ta import TaTokenizer

     try:
          if not is_tokenizers_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .tokenization_ta_fast import TaTokenizerFast

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_ta import (
              T5_PRETRAINED_MODEL_ARCHIVE_LIST,
              TaEncoderModel,
              TaForConditionalGeneration,
              TaForQuestionAnswering,
              TaModel,
              TaPreTrainedModel,
              load_tf_weights_in_ta,
          )

     try:
          if not is_tf_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_tf_ta import (
              TF_T5_PRETRAINED_MODEL_ARCHIVE_LIST,
              TFTaEncoderModel,
              TFTaForConditionalGeneration,
              TFTaModel,
              TFTaPreTrainedModel,
          )

     try:
          if not is_flax_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_flax_ta import (
              FlaxTaEncoderModel,
              FlaxTaForConditionalGeneration,
              FlaxTaModel,
              FlaxTaPreTrainedModel,
          )


else:
     import sys

     A__ :		Dict					=_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)



