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4085. Largest Prime from Consecutive Prime Sum

My accepted Python solution to LeetCode problem 4085, Largest Prime from Consecutive Prime Sum, running in 6430ms.

  • Difficulty: Medium
  • Python
  • Runtime 6430ms
  • Memory 22.3MB

Read the problem on LeetCode View on GitHub

The problem statement is LeetCode’s and stays on their site. What follows is my accepted solution.

Python

Accepted on LeetCode — runtime 6430ms, memory 22.3MB, accepted 2025-12-29.

python
class Solution:
    def largestPrime(self, n: int) -> int:
        # Sieve of Eratosthenes
        is_prime = [True] * (n + 1)
        is_prime[0] = is_prime[1] = False
        for i in range(2, int(n**0.5) + 1):
            if is_prime[i]:
                for j in range(i*i, n + 1, i):
                    is_prime[j] = False
        
        # Get list of primes <= n
        primes = [i for i in range(2, n + 1) if is_prime[i]]
        
        if not primes:
            return 0
        
        # Find all consecutive prime sums STARTING FROM 2 that are prime and <= n
        result = 0
        current_sum = 0
        
        for p in primes:
            current_sum += p
            if current_sum > n:
                break
            if is_prime[current_sum]:
                result = current_sum
        
        return result

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