



'''simple docstring'''







import math
def 			_lowerCAmelCase(      UpperCAmelCase_      :	Any						) ->							Union[str, Any]:

							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 			_lowerCAmelCase(      UpperCAmelCase_      :	Union[str, Any] = 1000					, UpperCAmelCase_      :	Union[str, Any] = 1000						) ->							Optional[int]:
							lowerCAmelCase__  =   [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_						):
																												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(1000, 1000))











from unittest.mock import patch

import datasets
from datasets import Dataset



def    UpperCAmelCase__	(  ):
  lowercase     :Any   						=    Dataset.from_dict({"col_1": [3, 2, 0, 1]} )

  with patch("tqdm.auto.tqdm" ) as mock_tqdm:
    datasets.disable_progress_bar()
    dset.map(lambda lowerCamelCase : {"col_2": x["col_1"] + 1} )
    mock_tqdm.assert_not_called()

    mock_tqdm.reset_mock()

    datasets.enable_progress_bar()
    dset.map(lambda lowerCamelCase : {"col_2": x["col_1"] + 1} )
    mock_tqdm.assert_called()



