Closest Prime Numbers in Range — LeetCode 2523 Python Solution

The problem

Given two positive integers left and right, find the two integers num1 and num2 such that: left <= num1 < num2 <= right . Both num1 and num2 are prime numbers.

Example

Input

left = 10, right = 19

Output

[11,13]

Explanation

The prime numbers between 10 and 19 are 11, 13, 17, and 19.

Python solution

class Solution:
    def closestPrimes(self, left: int, right: int) -> List[int]:
        cnt = 0
        st = [False] * (right + 1)
        prime = [0] * (right + 1)
        for i in range(2, right + 1):
            if not st[i]:
                prime[cnt] = i
                cnt += 1
            j = 0
            while prime[j] <= right // i:
                st[prime[j] * i] = 1
                if i % prime[j] == 0:
                    break
                j += 1
        p = [v for v in prime[:cnt] if left <= v <= right]
        mi = inf
        ans = [-1, -1]
        for a, b in pairwise(p):
            if (d := b - a) < mi:
                mi = d
                ans = [a, b]
        return ans

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 2523. Closest Prime Numbers in Range 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.

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