What is the optimal time complexity of solving Prime number?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Prime number?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Prime number?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Prime number?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

Back to Practice Dashboard

Python BasicsEasy

Prime number

Learn how to solve the 'Prime number' problem. This detailed resource details brute force and optimized approaches.

Mode Selected

Problem Statement

Easy

Write a function is_prime(n) that takes a positive integer n and returns True if n is a prime number, or False otherwise. A prime number is a number greater than 1 that has no divisors other than 1 and itself.

Constraints

•1 <= n <= 10^6

Examples

Example 1

Input

n = 7

Output

True

Explanation

7 is only divisible by 1 and 7, so it is prime.

Example 2

Input

n = 4

Output

False

Explanation

4 is divisible by 2 (4 = 2 × 2), so it is not prime.

Example 3

Input

n = 1

Output

False

Explanation

1 is not considered a prime number by definition.

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

Ready to Solve?

Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.

Open in Editor