5 Check Prime
Problem Statement
Write a Recursive Solution to Check if a Given Number is a Prime Number or Not.
Given a positive integer, we need to determine whether it is a prime number or not. A prime number is a number greater than 1 that has no positive divisors other than 1 and the number itself.
The following table describes three example outputs for three inputs along with the description:
| Input(s) | Output(s) | Explanation |
|---|---|---|
| Number = 7 | Is Prime = true | The number 7 is only divisible by 1 and 7, so it is a prime number. |
| Number = 12 | Is Prime = false | The number 12 is divisible by 1, 2, 3, 4, 6, and 12, so it is not a prime number. |
| Number = 23 | Is Prime = true | The number 23 is only divisible by 1 and 23, so it is a prime number. |
Constraints:
- 0 <= n <= 109
Try it yourself
Try solving this question here:
🎯 STRICT STANDOUT — Problem cue: Check Prime
1. Why
Trial division can be recursive (i, then i+1) but stack is unnecessary — teaches when-NOT recursion.
2. Big-O (K11)
Trial to √n: Θ(√n) checks; recursive i version depth Θ(√n) BAD; loop Θ(1) space3. Pattern + when-NOT
TRIAL DIVISION — prefer iterative. Batch primes → sieve not per-n recursion.
4. Edge
n<2 false; 2,3 true; 4 false; 9 false; 17 true5. Panel
Q: Why recursive prime is a smell? A: √n depth for no structural gain.
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