"""
We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once.
For example, 2143 is a 4-digit pandigital and is also prime.

What is the largest n-digit pandigital prime that exists?
"""

import random
import time
from functools import lru_cache
from itertools import permutations


def timer(func):
    def wrapper(*args, **kwargs):
        start_time = time.perf_counter()
        result = func(*args, **kwargs)
        end_time = time.perf_counter()
        print(f"Execution time: {end_time - start_time} seconds")
        return result

    return wrapper


def miller_rabin_test(n: int, k: int = 10) -> bool:
    if n < 2:
        return False
    if n == 2 or n == 3:
        return True
    if n % 2 == 0 or n % 3 == 0:
        return False
    r, s = 0, n - 1
    while s % 2 == 0:
        r += 1
        s //= 2
    for _ in range(k):
        a = random.randrange(2, n - 1)
        x = pow(a, s, n)
        if x == 1 or x == n - 1:
            continue
        for _ in range(r - 1):
            x = pow(x, 2, n)
            if x == n - 1:
                break
        else:
            return False
    return True


@lru_cache(maxsize=128)
def is_even_or_five_ending(num: int) -> bool:
    """快速检查是否为偶数或以5结尾"""
    return num % 2 == 0 or num % 5 == 0


@timer
def main() -> None:
    str_nums = "987654321"
    stop = False
    for i in range(9, 0, -1):
        if sum(int(digit) for digit in str_nums[-i:]) % 3 == 0:
            continue
        for perm in permutations(str_nums[-i:], i):
            num = int("".join(perm))
            if is_even_or_five_ending(num):
                continue
            if miller_rabin_test(num):
                print(num)
                stop = True
                break
        if stop:
            break


if __name__ == "__main__":
    main()