code: 
  
  
  """simple docstring"""
  import math
  
  def 							_snake_case			(      __snake_case       :			int      ):
  
  
  
  
     """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(__snake_case      ) + 1      )	,   6      ):
        if number % i == 0 or number % (i + 2) == 0:
           return False
     return True
  
  def 							_snake_case			(      __snake_case       :			int = 1000	,   __snake_case       :			int = 1000      ):
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     _lowerCamelCase  :				Optional[int]      =		[0, 0, 0]  # length, a, b
     for a in range((a_limit * -1) + 1	,   __snake_case      ):
        for b in range(2	,   __snake_case      ):
           if is_prime(__snake_case      ):
              _lowerCamelCase  :				Union[str, Any]      =		0
              _lowerCamelCase  :				Union[str, Any]      =		0
              while is_prime((n**2) + (a * n) + b      ):
                 count += 1
                 n += 1
              if count > longest[0]:
                 _lowerCamelCase  :				Optional[int]      =		[count, a, b]
     _lowerCamelCase  :				int      =		longest[1] * longest[2]
     return ans
  
  
  if __name__ == "__main__":
   print(solution(1000, 1000))
  
  
style_context: 
  
  
  """simple docstring"""
  import timeit
  
  
  
  
  class   lowercase__							:
  
  
  
  
  
     def __init__(       self			,      SCREAMING_SNAKE_CASE)     ->     Tuple:
        if isinstance(SCREAMING_SNAKE_CASE			,      SCREAMING_SNAKE_CASE):  # Initializes a matrix identical to the one provided.
           _lowerCamelCase  :				List[str]      =		arg
           _lowerCamelCase  :				List[str]      =		len(SCREAMING_SNAKE_CASE)
        else:  # Initializes a square matrix of the given size and set values to zero.
           _lowerCamelCase  :				List[Any]      =		arg
           _lowerCamelCase  :				Union[str, Any]      =		[[0 for _ in range(self.n)] for _ in range(self.n)]
  
  
  
  
  
     def __mul__(       self			,      SCREAMING_SNAKE_CASE)     ->     Optional[Any]:
        _lowerCamelCase  :				List[Any]      =		Matrix(self.n)
        for i in range(self.n):
           for j in range(self.n):
              for k in range(self.n):
                 matrix.t[i][j] += self.t[i][k] * b.t[k][j]
        return matrix
  
  
  
  
  
  
  
  def 							_snake_case			(      __snake_case       :			Union[str, Any]	,   __snake_case       :			List[Any]      ):
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     _lowerCamelCase  :				List[Any]      =		Matrix([[1, 0], [0, 1]]      )
     while b > 0:
        if b & 1:
           matrix *= a
        a *= a
        b >>= 1
     return matrix
  
  def 							_snake_case			(      __snake_case       :			List[str]	,   __snake_case       :			str	,   __snake_case       :			List[Any]      ):
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     if n == 1:
        return fa
     elif n == 2:
        return fa
     _lowerCamelCase  :				Any      =		Matrix([[1, 1], [1, 0]]      )
     _lowerCamelCase  :				List[str]      =		modular_exponentiation(__snake_case	,   n - 2      )
     return fa * matrix.t[0][0] + fa * matrix.t[0][1]
  
  def 							_snake_case			(      __snake_case       :			int	,   __snake_case       :			Optional[int]	,   __snake_case       :			List[Any]      ):
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     if n == 1:
        return fa
     elif n == 2:
        return fa
  
     _lowerCamelCase  :				Optional[Any]      =		fa
     _lowerCamelCase  :				int      =		fa
     n -= 2
  
     while n > 0:
        _lowerCamelCase      ,						_lowerCamelCase  :				Tuple      =		fn_a + fn_a, fn_a
        n -= 1
  
     return fn_a
  
  def 							_snake_case			(      ):
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     _lowerCamelCase  :				List[str]      =		"""
  from random import randint
  from __main__ import fibonacci_with_matrix_exponentiation
  """
     _lowerCamelCase  :				int      =		"""fibonacci_with_matrix_exponentiation(randint(1,70000), 1, 1)"""
     _lowerCamelCase  :				Tuple      =		timeit.timeit(setup=__snake_case	,   stmt=__snake_case	,   number=100      )
     print("""With matrix exponentiation the average execution time is """	,   exec_time / 100      )
     return exec_time
  
  def 							_snake_case			(      ):
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     _lowerCamelCase  :				Dict      =		"""
  from random import randint
  from __main__ import simple_fibonacci
  """
     _lowerCamelCase  :				Optional[int]      =		"""simple_fibonacci(randint(1,70000), 1, 1)"""
     _lowerCamelCase  :				List[Any]      =		timeit.timeit(setup=__snake_case	,   stmt=__snake_case	,   number=100      )
     print(
         """Without matrix exponentiation the average execution time is """	,   exec_time / 100      )
     return exec_time
  
  def 							_snake_case			(      ):
  
  
  
  
     """simple docstring"""
  
  
  
  
  
  
  
     matrix_exponentiation_time()
     simple_fibonacci_time()
  
  
  if __name__ == "__main__":
   main()
  
  