1. **Stating the problem:** We want to identify prime numbers easily. 2. **Definition:** A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. 3. **Basic rule:** To check if a number $n$ is prime, test divisibility by all integers from 2 up to $\sqrt{n}$. 4. **Why up to $\sqrt{n}$?** If $n$ has a divisor larger than $\sqrt{n}$, it must also have a smaller one, so checking beyond $\sqrt{n}$ is redundant. 5. **Step-by-step method:** - Calculate $\sqrt{n}$. - Check if $n$ is divisible by any integer $k$ where $2 \leq k \leq \lfloor \sqrt{n} \rfloor$. - If divisible by any such $k$, $n$ is not prime. - Otherwise, $n$ is prime. 6. **Example:** Check if 29 is prime. - Calculate $\sqrt{29} \approx 5.38$. - Test divisibility by 2, 3, 4, 5. - 29 is not divisible by any of these. - Therefore, 29 is prime. 7. **Additional tips:** - All primes greater than 2 are odd. - You can skip even numbers when testing divisibility. - Use known small primes to speed up checks. This method is efficient for small to moderately large numbers and helps identify primes easily.