Closest Prime Numbers in Range

Closest Prime Numbers in Range - 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
num2 - num1 is the minimum amongst all other pairs satisfying the above conditions

Return the positive integer array ans = [num1, num2]. If there are multiple pairs satisfying these conditions, return the one with the smallest num1 value. If no such numbers exist, return [-1, -1].

Input & Output

Example 1 — Basic Range

$ Input: left = 4, right = 6

› Output: [-1, -1]

💡 Note: Only prime in range [4,6] is 5. Since we need two different primes with num1 < num2, no valid pair exists.

Example 2 — Twin Primes

$ Input: left = 4, right = 18

› Output: [5, 7]

💡 Note: Primes in range [4,18]: 5, 7, 11, 13, 17. Gaps between consecutive primes: 7-5=2, 11-7=4, 13-11=2, 17-13=4. Minimum gap is 2, first occurrence is [5, 7]

Example 3 — Large Gap

$ Input: left = 20, right = 30

› Output: [23, 29]

💡 Note: Primes in range [20,30]: 23, 29. Only one pair possible: [23, 29] with gap 6

Constraints

1 ≤ left ≤ right ≤ 10⁶
Both left and right are positive integers

Visualization

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Asked in

G Google 25 M Microsoft 20 a Amazon 15

The key insight is to efficiently find all primes in the range using Sieve of Eratosthenes, then scan consecutive primes to find the minimum gap. The optimal approach uses sieve for O(n log log n) prime generation, then linear scan for closest pair. Time: O(n log log n), Space: O(n).

Common Approaches

✓ Brute Force Prime Checking

⏱️ Time: O(n²√n) Space: O(n)

For each number in the range, check if it's prime by testing divisibility up to its square root. Then compare all prime pairs to find the minimum gap.

Sieve of Eratosthenes + Linear Scan

⏱️ Time: O(n log log n) Space: O(n)

Use Sieve of Eratosthenes to efficiently find all primes up to 'right', then scan consecutive primes in the range to find the pair with minimum gap.

Brute Force Prime Checking — Algorithm Steps

Step 1: Create helper function to check if number is prime
Step 2: Find all primes in range [left, right]
Step 3: Compare all pairs to find minimum gap

Visualization

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Step-by-Step Walkthrough

Prime Check

Test each number for primality

Collect Primes

Gather all prime numbers found

Find Minimum Gap

Compare all pairs to find closest

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <limits.h>

int isPrime(int n) {
    if (n < 2) return 0;
    if (n == 2) return 1;
    if (n % 2 == 0) return 0;
    for (int i = 3; i <= sqrt(n); i += 2) {
        if (n % i == 0) return 0;
    }
    return 1;
}

void solution(int left, int right, int* result) {
    int* primes = (int*)malloc(10000 * sizeof(int));
    int count = 0;
    
    for (int num = left; num <= right; num++) {
        if (isPrime(num)) {
            primes[count++] = num;
        }
    }
    
    if (count < 2) {
        result[0] = -1;
        result[1] = -1;
        free(primes);
        return;
    }
    
    int minGap = INT_MAX;
    result[0] = -1;
    result[1] = -1;
    
    for (int i = 0; i < count; i++) {
        for (int j = i + 1; j < count; j++) {
            int gap = primes[j] - primes[i];
            if (gap < minGap) {
                minGap = gap;
                result[0] = primes[i];
                result[1] = primes[j];
            }
        }
    }
    
    free(primes);
}

int main() {
    int left, right;
    scanf("%d", &left);
    scanf("%d", &right);
    
    int result[2];
    solution(left, right, result);
    
    printf("[%d,%d]\n", result[0], result[1]);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n²√n)

For each of n numbers, check primality in O(√n), then compare O(n²) pairs

⚠ Quadratic Growth

Space Complexity

O(n)

Store list of primes found in the range

⚡ Linearithmic Space

23.4K Views

Medium Frequency

~25 min Avg. Time

890 Likes

Ln 1, Col 1

Smart Actions

💡 Explanation

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Input & Output

Constraints

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Related Problems

Common Approaches

Brute Force Prime Checking — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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