Which of the following numbers can be used to show that not all prime numbers are odd?

Introduction / Context:
This question checks your basic understanding of prime numbers and a very important exception related to even numbers. Many people think that all primes are odd, and this item directly challenges that misconception using a simple example.

Given Data / Assumptions:

• We are given four small integers: 1, 2, 3 and 4.
• We must choose the number that shows that not all prime numbers are odd.
• A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself.

Concept / Approach:
The key concept is the definition of prime numbers and the special role of the number 2. All even numbers greater than 2 are composite, but 2 is a unique even number that is still prime. This single example is enough to disprove the statement that all primes are odd, because a single counterexample is sufficient.

Step-by-Step Solution:
Step 1: Check if 1 is prime. The number 1 has only one positive divisor (itself), so it does not meet the definition of a prime (which requires two distinct divisors). So 1 is not prime.Step 2: Check if 2 is prime. The divisors of 2 are 1 and 2. That gives exactly two distinct positive divisors, so 2 is prime.Step 3: Check the parity of 2. The number 2 is even because it is divisible by 2.Step 4: Since 2 is an even prime, it is a counterexample to the claim that all primes are odd.Step 5: Verify remaining numbers: 3 is prime but odd, and 4 is composite (divisible by 1, 2 and 4). They do not help disprove the claim that all primes are odd.

Verification / Alternative check:
You can list the first few prime numbers: 2, 3, 5, 7, 11, 13, ... All except 2 are odd, and 2 is clearly even, so it is a simple visual check that not all prime numbers are odd.

Why Other Options Are Wrong:
1 is not prime under the standard definition, so it cannot be used to illustrate anything about prime parity.3 is prime but it is odd, so it does not disprove the claim that all primes are odd.4 is an even number but it is composite, not prime, so it does not work as a counterexample either.

Common Pitfalls:
Some learners still incorrectly treat 1 as a prime number, which leads to confusion in number theory.Others forget that a single counterexample (like 2) is enough to disprove a general statement.Remember that 2 is the only even prime number; every other even number has at least three divisors and is therefore composite.

Final Answer:
The number 2 shows that not all prime numbers are odd.