


'''simple docstring'''

import math



def 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					int )		->       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 							SCREAMING_SNAKE_CASE__(		_UpperCamelCase   :					int = 10_00     ,		_UpperCamelCase   :					int = 10_00 )		->       int:





   '''simple docstring'''







   UpperCamelCase__			    =    [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 ):
            UpperCamelCase__			    =    0
            UpperCamelCase__			    =    0
            while is_prime((n**2) + (a * n) + b ):
               count += 1
               n += 1
            if count > longest[0]:
               UpperCamelCase__			    =    [count, a, b]
   UpperCamelCase__			    =    longest[1] * longest[2]
   return ans


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




import sys
from dataclasses import dataclass
from typing import TYPE_CHECKING, Dict, List, Optional, Tuple, Union

import pandas as pd
import pyarrow as pa

import datasets
import datasets.config
from datasets.features.features import require_storage_cast
from datasets.table import table_cast


if TYPE_CHECKING:
				import sqlitea

				import sqlalchemy


_lowercase:					Optional[Any]      =						datasets.utils.logging.get_logger(__name__)



@dataclass
class       _lowercase				(  datasets.BuilderConfig      ):





	"""simple docstring"""
	__A		      =				None
	__A		      =				None
	__A		      =				None
	__A		      =				True
	__A		      =				None
	__A		      =				None
	__A		      =				None
	__A		      =				10000
	__A		      =				None




	def 	UpperCamelCase_			(self						):
						"""simple docstring"""

						if self.sql is None:
											raise ValueError("sql must be specified"						)
						if self.con is None:
											raise ValueError("con must be specified"						)




	def 	UpperCamelCase_			(self						,			lowerCamelCase_						,			lowerCamelCase_ = None						,			):
						"""simple docstring"""

						a   	=  config_kwargs.copy()
						# We need to stringify the Selectable object to make its hash deterministic

						# The process of stringifying is explained here: http://docs.sqlalchemy.org/en/latest/faq/sqlexpressions.html
						a   	=  config_kwargs["sql"]
						if not isinstance(lowerCamelCase_						,			lowerCamelCase_						):
											if datasets.config.SQLALCHEMY_AVAILABLE and "sqlalchemy" in sys.modules:
																import sqlalchemy

																if isinstance(lowerCamelCase_						,			sqlalchemy.sql.Selectable						):
																					a   	=  sqlalchemy.create_engine(config_kwargs["con"].split("://"						)[0] + "://"						)
																					a   	=  str(sql.compile(dialect=engine.dialect						)						)
																					a   	=  sql_str
																else:
																					raise TypeError(
																					    F'''Supported types for \'sql\' are string and sqlalchemy.sql.Selectable but got {type(lowerCamelCase_						)}: {sql}'''						)
											else:
																raise TypeError(
																    F'''Supported types for \'sql\' are string and sqlalchemy.sql.Selectable but got {type(lowerCamelCase_						)}: {sql}'''						)
						a   	=  config_kwargs["con"]
						if not isinstance(lowerCamelCase_						,			lowerCamelCase_						):
											a   	=  id(lowerCamelCase_						)
											logger.info(
											    F'''SQL connection \'con\' of type {type(lowerCamelCase_						)} couldn\'t be hashed properly. To enable hashing, specify \'con\' as URI string instead.'''						)

						return super().create_config_id(lowerCamelCase_						,			custom_features=lowerCamelCase_						)




	@property
	def 	UpperCamelCase_			(self						):
						"""simple docstring"""

						a   	=  {
						    "index_col": self.index_col,
						    "columns": self.columns,
						    "params": self.params,
						    "coerce_float": self.coerce_float,
						    "parse_dates": self.parse_dates,
						}
						return pd_read_sql_kwargs




class       _lowercase				(  datasets.ArrowBasedBuilder      ):





	"""simple docstring"""
	__A		      =				SqlConfig




	def 	UpperCamelCase_			(self						):
						"""simple docstring"""

						return datasets.DatasetInfo(features=self.config.features						)




	def 	UpperCamelCase_			(self						,			lowerCamelCase_						):
						"""simple docstring"""

						return [datasets.SplitGenerator(name=datasets.Split.TRAIN						,			gen_kwargs={}						)]




	def 	UpperCamelCase_			(self						,			lowerCamelCase_						):
						"""simple docstring"""

						if self.config.features is not None:
											a   	=  self.config.features.arrow_schema
											if all(not require_storage_cast(lowerCamelCase_						) for feature in self.config.features.values()						):
																# cheaper cast
																a   	=  pa.Table.from_arrays([pa_table[field.name] for field in schema]						,			schema=lowerCamelCase_						)
											else:
																# more expensive cast; allows str <-> int/float or str to Audio for example
																a   	=  table_cast(lowerCamelCase_						,			lowerCamelCase_						)
						return pa_table




	def 	UpperCamelCase_			(self						):
						"""simple docstring"""

						a   	=  self.config.chunksize
						a   	=  pd.read_sql(
						    self.config.sql						,			self.config.con						,			chunksize=lowerCamelCase_						,			**self.config.pd_read_sql_kwargs						)
						a   	=  [sql_reader] if chunksize is None else sql_reader
						for chunk_idx, df in enumerate(lowerCamelCase_						):
											a   	=  pa.Table.from_pandas(lowerCamelCase_						)
											yield chunk_idx, self._cast_table(lowerCamelCase_						)
