import math


def prime_range(n: int) -> list:
    """
    Gets a range that the nth prime can reasonably be expected to be in
    Found the formula (from the Prime Number Theorem) here:
    https://math.stackexchange.com/questions/1257/is-there-a-known-mathematical-equation-to-find-the-nth-prime

    :param n: The index for a prime number
    :returns: A list with the lower an upper limit that the nth prime
              number can be expected to be in
    """

    # Note: math.log() returns the natural log if no base is specified
    range_min = n * math.log(n) + n * (math.log(math.log(n)) - 1)
    range_max = n * math.log(n) + n * math.log(math.log(n))
    return [math.ceil(range_min), math.ceil(range_max)]