






import math

def        _lowerCamelCase		(  __A      :							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(__A	) + 1	)						,						6	):
        if number % i == 0 or number % (i + 2) == 0:
            return False
    return True

def        _lowerCamelCase		(  __A      :							int = 1_000						,						__A      :							int = 1_000	) ->   int:
    _UpperCAmelCase			: Dict     					=			[0, 0, 0]  # length, a, b
    for a in range((a_limit * -1) + 1						,						__A	):
        for b in range(2						,						__A	):
            if is_prime(__A	):
                _UpperCAmelCase			: Any     					=			0
                _UpperCAmelCase			: List[Any]     					=			0
                while is_prime((n**2) + (a * n) + b	):
                    count += 1
                    n += 1
                if count > longest[0]:
                    _UpperCAmelCase			: Union[str, Any]     					=			[count, a, b]
    _UpperCAmelCase			: Tuple     					=			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        _lowerCamelCase		(  ) ->   Tuple:
    _UpperCAmelCase			: Union[str, 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 __A	: {"col_2": x["col_1"] + 1}	)
        mock_tqdm.assert_not_called()

        mock_tqdm.reset_mock()

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




