Mathematical Investigation: Spotting Prime Numbers

To solve this problem, we'll verify whether each number is a prime number:

• 22: Divisible by 2. Not a prime number.

• 23: Divisible only by 1 and 23. It is a prime number.

• 21: Divisible by 3 and 7. Not a prime number.

• 24: Divisible by 2. Not a prime number.

Now, let's go through each step in detail:

Step 1: Check 22
22 is even, meaning it is divisible by 2. As it has divisors other than 1 and itself, 22 is not a prime number.

Step 2: Check 23
Begin by testing divisibility by 2. Since 23 is odd, it is not divisible by 2. Next, check divisibility by 3: $23 \div 3 \approx 7.67$, not an integer. No divisors other than 1 and 23 are found, therefore 23 is a prime number.

Step 3: Check 21
21 is odd, so not divisible by 2. However, $21 \div 3 = 7$, which is an integer. Thus, 21 is not prime because it is divisible by numbers other than 1 and itself.

Step 4: Check 24
24 is even and divisible by 2. Hence, 24 is not a prime number.

Therefore, the solution to the problem is $23$.