Project Euler 808

题目

Reversible prime squares

Both \(169\) and \(961\) are the square of a prime. \(169\) is the reverse of \(961\).

We call a number a reversible prime square if:

1. It is not a palindrome, and
2. It is the square of a prime, and
3. Its reverse is also the square of a prime.

\(169\) and \(961\) are not palindromes, so both are reversible prime squares.

Find the sum of the first \(50\) reversible prime squares.

解决方案

直接使用sympy库中的nextprime暴力枚举质数进行判断，需要注意不要漏掉第一个条件。

代码

from tools import is_prime, is_square, int_sqrt
from sympy import nextprime

N = 50


def ok(n):
    s = str(n)
    t = s[::-1]
    if s == t:
        return False
    m = int(t)
    return is_prime(int_sqrt(m)) if is_square(m) else False


p = 1
ans = 0
while True:
    p = nextprime(p)
    if ok(p * p):
        ans += p * p
        N -= 1
        if N == 0:
            break
print(ans)