



import math
from decimal import Decimal, getcontext
def 	lowercase_							(A			:			int = 4_0_0_0_0_0_0				):

       try:
              snake_case__							:     List[Any]            =     int(A				)
       except (TypeError, ValueError):
              raise TypeError('Parameter n must be int or castable to int.'				)
       if n <= 0:
              raise ValueError('Parameter n must be greater than or equal to one.'				)
       snake_case__							:     Dict            =     1_0_0
       snake_case__							:     Any            =     (Decimal(5				) ** Decimal(0.5				) + 1) / Decimal(2				)

       snake_case__							:     List[Any]            =     (math.floor(math.log(n * (phi + 2)		, A				) - 1				) // 3) * 3 + 2
       snake_case__							:     List[str]            =     Decimal(round(phi ** Decimal(index + 1				)				)				) / (phi + 2)
       snake_case__							:     Dict            =     num // 2
       return int(A				)


if __name__ == "__main__":
 print(F"""{solution() = }""")











import math
def 	lowercase_							(A			:			int				):

       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 	lowercase_							(A			:			int = 1_0_0_0		, A			:			int = 1_0_0_0				):
       snake_case__							:     str            =     [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				):
                            snake_case__							:     Optional[Any]            =     0
                            snake_case__							:     Optional[int]            =     0
                            while is_prime((n**2) + (a * n) + b				):
                                   count += 1
                                   n += 1
                            if count > longest[0]:
                                   snake_case__							:     Union[str, Any]            =     [count, a, b]
       snake_case__							:     List[str]            =     longest[1] * longest[2]
       return ans


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






