"""
The arithmetic sequence, 1487,4817,8147, in which each of the terms increases by 3330,
is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the
4-digit numbers are permutations of one another.

There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property,
but there is one other 4-digit increasing sequence.

What 12-digit number do you form by concatenating the three terms in this sequence?
"""

import time


def timer(func):
    def wrapper(*args, **kwargs):
        start_time = time.time()
        result = func(*args, **kwargs)
        end_time = time.time()
        elapsed_time = end_time - start_time
        print(f"{func.__name__} time: {elapsed_time:.6f} seconds")
        return result

    return wrapper


def list_primes(start: int, end: int) -> list[int]:
    # 只需要筛到 sqrt(9999) ≈ 100 即可标记合数
    limit = int(end**0.5) + 1
    base_primes = [True] * limit
    base_primes[0] = base_primes[1] = False

    # 生成基础质数（2到100）
    for i in range(2, int(limit**0.5) + 1):
        if base_primes[i]:
            for j in range(i * i, limit, i):
                base_primes[j] = False

    # 分段筛：只标记1000-9999范围
    size = end - start + 1
    is_prime = [True] * size

    for p in range(2, limit):
        if base_primes[p]:
            # 找到第一个大于等于start的p的倍数
            first = max(p * p, ((start + p - 1) // p) * p)
            for j in range(first, end + 1, p):
                is_prime[j - start] = False

    return [i + start for i, val in enumerate(is_prime) if val]


def list_com(a: list, b: list) -> bool:
    if len(set(a)) != len(set(b)):
        return False
    xb = b.copy()
    for x in a:
        if x not in xb:
            return False
        else:
            xb.remove(x)
    return True


@timer
def main():
    primes = list_primes(1000, 9999)
    max_sp = max(primes)
    res = []
    for i, v in enumerate(primes):
        if v == max_sp:
            break
        gap = int((max_sp - v) / 3)
        for g in range(gap, (primes[i + 1] - v - 1), -1):
            if v + g in primes and v + 2 * g in primes:
                if list_com(list(str(v)), list(str(v + g))):
                    if list_com(list(str(v)), list(str(v + 2 * g))):
                        res.append(str(v) + str(v + g) + str(v + 2 * g))
                else:
                    continue
    print(res)


if __name__ == "__main__":
    main()