Prime Pairs With Target Sum — LeetCode 2761 Python Solution

The problem

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].

Example

Input

n = 10

Output

[[3,7],[5,5]]

Explanation

In this example, there are two prime pairs that satisfy the criteria.

Python solution

class Solution:
    def findPrimePairs(self, n: int) -> List[List[int]]:
        primes = [True] * n
        for i in range(2, n):
            if primes[i]:
                for j in range(i + i, n, i):
                    primes[j] = False
        ans = []
        for x in range(2, n // 2 + 1):
            y = n - x
            if primes[x] and primes[y]:
                ans.append([x, y])
        return ans

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 2761. Prime Pairs With Target Sum 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.

Related problems