# Solving Leetcode Interviews in Seconds with AI: Prime Pairs With Target Sum


	# Introduction
	In this blog post, we will explore how to solve the LeetCode problem "2761" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like [Chatmagic](https://www.chatmagic.app), we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

	# Problem Statement
	> You are given an integer n. We say that two integers x and y form a prime number pair if:  1 <= x <= y <= n x + y == n x and y are prime numbers  Return the 2D sorted list of prime number pairs [xi, yi]. The list should be sorted in increasing order of xi. If there are no prime number pairs at all, return an empty array. Note: A prime number is a natural number greater than 1 with only two factors, itself and 1.   Example 1:  Input: n = 10 Output: [[3,7],[5,5]] Explanation: In this example, there are two prime pairs that satisfy the criteria.  These pairs are [3,7] and [5,5], and we return them in the sorted order as described in the problem statement.  Example 2:  Input: n = 2 Output: [] Explanation: We can show that there is no prime number pair that gives a sum of 2, so we return an empty array.     Constraints:  1 <= n <= 106  

	# Explanation
	Here's the approach, complexity analysis, and Python code for the prime number pair problem:

*   **Sieve of Eratosthenes:** Use the Sieve of Eratosthenes to efficiently precompute all prime numbers up to `n`. This avoids repeated primality tests.
*   **Iterate and Check:** Iterate through numbers from 2 up to `n // 2`. For each number `x`, check if both `x` and `n - x` are prime using the precomputed prime table.
*   **Sorted Pairs:** If both are prime, add the pair `[x, n - x]` to the result list. The iteration ensures the list is sorted by the first element.

*   **Runtime Complexity:** O(n log log n) for Sieve of Eratosthenes + O(n/2) for iteration and checking. Dominates to O(n log log n).
*   **Storage Complexity:** O(n) for storing the prime table.

	
	# Code
	```python
	def prime_number_pairs(n: int) -> list[list[int]]:
    """
    Given an integer n. We say that two integers x and y form a prime number pair if:

    1 <= x <= y <= n
    x + y == n
    x and y are prime numbers

    Return the 2D sorted list of prime number pairs [xi, yi]. The list should be sorted in increasing order of xi.
    If there are no prime number pairs at all, return an empty array.

    Note:
    A prime number is a natural number greater than 1 with only two factors, itself and 1.

    For example:
    prime_number_pairs(10) == [[3, 7], [5, 5]]
    prime_number_pairs(2) == []
    """

    if n < 2:
        return []

    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

    result = []
    for x in range(2, n // 2 + 1):
        if is_prime[x] and is_prime[n - x]:
            result.append([x, n - x])

    return result
	```