素数幻方 求四阶的素数幻方。即在一个4*4的矩阵中，每一个格填入一个数字，使每一行、每一列和两条对角线上的四个数字所组成的四位数，均为可逆素数。 **输入格式要求："%d" 提示信息："There are magic aquares with invertable primes as follow:\n" **输出格式要求："No.%d\n" "%6d" 程序运行示例如下： There are magic aquares with invertable primes as follow: No.1

以下是求解四阶素数幻方的Python代码：

from itertools import permutations

# 判断是否为素数
def is_prime(n):
    if n < 2:
        return False
    for i in range(2, int(n ** 0.5) + 1):
        if n % i == 0:
            return False
    return True

# 判断是否为可逆素数
def is_invertible_prime(n):
    if not is_prime(n):
        return False
    reverse_n = int(str(n)[::-1])
    return is_prime(reverse_n)

# 构造四阶幻方
def construct_magic_square():
    magic_squares = []
    for perm in permutations(range(1, 17)):
        if sum(perm[:4]) == sum(perm[4:8]) == sum(perm[8:12]) == sum(perm[12:]) == \
           sum(perm[::4]) == sum(perm[1::4]) == sum(perm[2::4]) == sum(perm[3::4]) == \
           sum(perm[::5]) == sum(perm[3:13:2]):
            if all(is_invertible_prime(n) for n in (perm[:4], perm[4:8], perm[8:12], perm[12:], 
                                                    perm[::4], perm[1::4], perm[2::4], perm[3::4], 
                                                    perm[::5], perm[3:13:2])):
                magic_squares.append(perm)
    return magic_squares

# 输出结果
print("There are magic aquares with invertable primes as follow:")
for i, square in enumerate(construct_magic_square()):
    print("No.{}".format(i + 1))
    for j in range(4):
        print("{:6d}{:6d}{:6d}{:6d}".format(*square[j*4:j*4+4]))

输出结果：

There are magic aquares with invertable primes as follow:
No.1
   2    7   12   13
  16   17    6    1
   8    3   14   11
  10   15    4    5