How do you solve Largest Prime from Consecutive Prime Sum on LeetCode?

Largest Prime from Consecutive Prime Sum (LeetCode #3770) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log log n) time complexity and O(n) space complexity. Key insight: Consecutive sums of primes can yield primes themselves.

What is the time complexity of Largest Prime from Consecutive Prime Sum?

The optimal solution for Largest Prime from Consecutive Prime Sum runs in O(n log log n) time and uses O(n) space. Sieve of Eratosthenes runs in O(n log log n) and we store primes in a set for O(1) lookups.

What is the brute force solution for Largest Prime from Consecutive Prime Sum?

The brute force approach for Largest Prime from Consecutive Prime Sum is Brute Force, with O(n²) time complexity and O(1) space complexity. We can find all prime numbers up to n and then check all possible sums of consecutive primes to see if they are prime and less than or equal to n. The optimal Optimal Solution approach improves this to O(n log log n).

What algorithm or data structure is used to solve Largest Prime from Consecutive Prime Sum?

Largest Prime from Consecutive Prime Sum uses the following concepts: Array, Math, Number Theory. The recommended patterns to study are: Sieve of Eratosthenes, Cumulative Sums.

What are the interview tips for Largest Prime from Consecutive Prime Sum?

Explain your thought process clearly. Consider edge cases early in your solution. Optimize your brute force solution into a more efficient approach.

What are common mistakes when solving Largest Prime from Consecutive Prime Sum?

Not checking if the cumulative sum exceeds n. Forgetting to handle edge cases like n = 2.

#3770

Largest Prime from Consecutive Prime Sum

Medium

ArrayMathNumber TheorySieve of EratosthenesCumulative Sums

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log log n)
Space	O(1)	O(n)

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Intuition

Time O(n log log n)Space O(n)

Use the Sieve of Eratosthenes to generate primes efficiently and compute their cumulative sums to find the largest prime sum.

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Algorithm

3 steps

1Step 1: Use the Sieve of Eratosthenes to generate all primes up to n.
2Step 2: Compute cumulative sums of these primes.
3Step 3: Check which of these sums are prime and less than or equal to n, returning the largest.

solution.py22 lines

1def sieve(n):
2    is_prime = [True] * (n + 1)
3    p = 2
4    while (p * p <= n):
5        if is_prime[p]:
6            for i in range(p * p, n + 1, p):
7                is_prime[i] = False
8        p += 1
9    return [p for p in range(2, n + 1) if is_prime[p]]
10
11def largest_prime_sum(n):
12    primes = sieve(n)
13    prime_set = set(primes)
14    cum_sum = 0
15    max_prime = 0
16    for prime in primes:
17        cum_sum += prime
18        if cum_sum > n:
19            break
20        if cum_sum in prime_set:
21            max_prime = max(max_prime, cum_sum)
22    return max_prime

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Complexity note: Sieve of Eratosthenes runs in O(n log log n) and we store primes in a set for O(1) lookups.

1Consecutive sums of primes can yield primes themselves.
2Using sets allows for quick prime existence checks.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.