🔥Most Efficient Solution✅||Full Explanation||✅≧◠‿◠≦✅||🧠Less Memory & Time
Intuition\n Describe your first thoughts on how to solve this problem. \nTo improve the time efficiency and handle the "Time Limit Exceeded" issue, we can optim
# Intuition\n<!-- Describe your first thoughts on how to solve this problem. -->\nTo improve the time efficiency and handle the "Time Limit Exceeded" issue, we can optimize the palindrome generation and primality testing steps. Instead of generating all palindromes up to a certain number, we can directly generate candidate palindromes and check their primality.\n\n# Approach\n<!-- Describe your approach to solving the problem. -->\n- **Generate palindrome candidates**: We\'ll generate palindromes starting from single-digit numbers and moving upwards.\n- **Check for primality**: We\'ll use an optimized primality check.\n- Stop as soon as we find a prime palindrome greater than or equal to n\n# Complexity\n- Time complexity: $O(Sqrt(N)\u2217Log(N))$\n\n\n---\n\n![image.png](https://assets.leetcode.com/users/images/5e0de8b1-de6a-4081-9aa1-e4103f943766_1719847375.9079638.png)\n\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->\n\n- Space complexity: $O(1)$\n\n---\n\n![Screenshot 2024-07-01 205226.png](https://assets.leetcode.com/users/images/c81a5a4e-cd38-4b58-9051-977b2ffb6cf0_1719847515.2682495.png)\n<!-- Add your space complexity here, e.g. $$O(n)$$ -->\n\n# Code\n```\nclass Solution:\n    def primePalindrome(self, n: int) -> int:\n        def is_palindrome(x):\n            s = str(x)\n            return s == s[::-1]\n\n        def is_prime(x):\n            if x < 2:\n                return False\n            if x == 2:\n                return True\n            if x % 2 == 0:\n                return False\n            for i in range(3, int(math.sqrt(x)) + 1, 2):\n                if x % i == 0:\n                    return False\n            return True\n\n        # Generate palindrome candidates\n        def generate_palindromes():\n            for i in range(1, 10):  # Single digit palindromes\n                yield i\n            for length in range(1, 6):  # Palindromes up to 10^8\n                # Odd length palindromes\n                for root in range(10**(length - 1), 10**length):\n                    s = str(root)\n                    yield int(s + s[-2::-1])\n                # Even length palindromes\n                for root in range(10**(length - 1), 10**length):\n                    s = str(root)\n                    yield int(s + s[::-1])\n\n        # Iterate over palindromes and find the smallest prime palindrome >= n\n        for palindrome in generate_palindromes():\n            if palindrome >= n and is_prime(palindrome):\n                return palindrome\n\n        return -1  # This should never happen with the given constraints\n\n\n\n```\n![ae7b6a0f-bc82-4c50-bede-27cdbb032188_1718672884.964757.png](https://assets.leetcode.com/users/images/8b7cf09d-d443-4f68-b2dc-940e4b5d0adb_1719847575.7146862.png)\n\n---\n\n> Thank You\n\n
['Python3']