Is 23 Prime or Composite? Number Classification Challenge

To determine whether $n = 23$ is a prime number, we will test its divisibility:

• Step 1: Calculate $\sqrt{23}$. The approximate value is 4.795, and thus we consider prime numbers up to the integer part, which is 4.
• Step 2: Check if 23 is divisible by any prime numbers less than or equal to 4. These primes are 2 and 3.

Step 3: Test divisibility:
- 23 is not divisible by 2, as it is odd.
- 23 is not divisible by 3, since $23 \div 3 \approx 7.67$, which is not an integer.

Since 23 is not divisible by any prime number less than or equal to its square root, it only has divisors of 1 and 23. Hence, 23 is a prime number.

Therefore, the solution to the problem is that $n = 23$ is prime.