





import math







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







def  lowerCAmelCase__(		lowercase    :      int = 1000				,       lowercase    :      int = 1000			)	->      int:
  __snake_case				:			Optional[int]            =    [0, 0, 0]  # length, a, b
  for a in range((a_limit * -1) + 1				,       lowercase			):
    for b in range(2				,       lowercase			):
      if is_prime(lowercase			):
        __snake_case				:			Optional[Any]            =    0
        __snake_case				:			Dict            =    0
        while is_prime((n**2) + (a * n) + b			):
          count += 1
          n += 1
        if count > longest[0]:
          __snake_case				:			Optional[int]            =    [count, a, b]
  __snake_case				:			Optional[Any]            =    longest[1] * longest[2]
  return ans


if __name__ == "__main__":
     print(solution(1000, 1000))








def  lowerCAmelCase__(		lowercase    :      int = 10**6			)	->      int:

  if n <= 0:
    raise ValueError("Please enter an integer greater than 0"			)

  __snake_case				:			List[Any]            =    list(range(n + 1			)			)
  for number in range(2				,       n + 1			):
    if phi[number] == number:
      phi[number] -= 1
      for multiple in range(number * 2				,       n + 1				,       lowercase			):
        __snake_case				:			Optional[int]            =    (phi[multiple] // number) * (number - 1)

  __snake_case				:			List[Any]            =    1
  for number in range(1				,       n + 1			):
    if (answer / phi[answer]) < (number / phi[number]):
      __snake_case				:			List[str]            =    number

  return answer


if __name__ == "__main__":
     print(solution())

