import random
import math
import sys


def even(n):
    return n % 2 == 0


# Use the Miller-Rabin algorithm to test primality of x
def is_prime(x, k):
    # Base cases
    if even(x):
        return False
    if x in [2, 3]:
        return True
    # Determine s and t
    s = 0
    t = x - 1
    while even(t):
        s += 1
        t //= 2
    # Gather witnesses
    witnesses = [random.randrange(2, x - 1) for _ in range(k)]
    for w in witnesses:
        if power_mod(w, x - 1, x) != 1:  # Basic Fermat test
            return False
        for i in range(1, s + 1):  # Advanced test if Fermat fails
            if power_mod(w, 2 ** i * t, x) == 1 and power_mod(w, 2 ** (i - 1) * t, x) not in [1, x - 1]:
                return False
    return True  # All witnesses must agree to get here


# Use repeated-squaring method to determine: base^power % mod
def power_mod(base, power, mod):
    binary = bin(power)
    squares = [base % mod]  # Start with base case
    result = squares[0] if binary[-1] == "1" else 1
    for i in range(1, math.floor(math.log2(power)) + 1):
        squares.append(squares[i - 1] ** 2 % mod)
        if binary[-i - 1] == "1":
            result *= squares[i]
    return result % mod


# Generate a twin prime of bit length m. Only tests values of 6x±1.
def generate_twin_prime(m):
    twin = False
    while not twin:
        start, end = bit_range(m)
        n = random.randrange(start + 6 - (start % 6), end, 6)  # Only test m bit ints that are multiples of 6
        num_witnesses = max(4, math.ceil(math.log(n, 4)))  # Based on probability 4^{-k} that a witness will be wrong.
        twin = is_prime(n - 1, num_witnesses) and is_prime(n + 1, num_witnesses)  # Check twin on either side of 6x
    return n - 1, n + 1


# Tuple containing range for bit length m
def bit_range(m):
    return 2 ** (m - 1), 2 ** m


# Write a twin in the correct format to file
def write_twin(twin):
    with open("output_twin_prime.txt", "w") as file:
        file.write(f"{twin[0]}\n{twin[1]}")


def main():
    assert len(sys.argv) >= 2
    twin = generate_twin_prime(int(sys.argv[1]))
    write_twin(twin)
    print(twin)


if __name__ == "__main__":
    main()