Prime Palindrome — LeetCode 866 Python Solution

The problem

Given an integer n, return the smallest prime palindrome greater than or equal to n. An integer is prime if it has exactly two divisors: 1 and itself.

Example

Input

n = 6

Output

7

Python solution

class Solution:
    def primePalindrome(self, n: int) -> int:
        def is_prime(x):
            if x < 2:
                return False
            v = 2
            while v * v <= x:
                if x % v == 0:
                    return False
                v += 1
            return True

        def reverse(x):
            res = 0
            while x:
                res = res * 10 + x % 10
                x //= 10
            return res

        while 1:
            if reverse(n) == n and is_prime(n):
                return n
            if 10**7 < n < 10**8:
                n = 10**8
            n += 1

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 866. Prime Palindrome is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math and Number Theory.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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