Question

The smallest prime number is

• A. 1
• B. 2
• C. 3
• D. 5

Hint:

Always remember that \(1\) is excluded from the set of prime numbers.
The set of prime numbers starts as: \(\{2, 3, 5, 7, 11, \dots\}\).
This makes \(2\) the smallest and only even prime number.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question tests basic number theory and definitions of mathematical terms, specifically the concept of prime numbers.

Step 2: Key Formulas and approach:
Define what constitutes a "prime number" based on its divisor properties.
Apply this definition sequentially starting from the lowest positive integers (\(1, 2, 3, \dots\)) to identify the smallest prime number.

Step 3: Detailed Explanation:

• A prime number is defined as a natural number greater than \(1\) that has no positive divisors other than \(1\) and itself.

• Let us evaluate the first few positive integers:

• The number \(1\) is neither prime nor composite by mathematical definition, because it does not have two distinct positive divisors (it only has one, which is itself).

• The number \(2\) is a natural number greater than \(1\) whose only positive divisors are \(1\) and \(2\). Thus, it satisfies the definition of a prime number perfectly.

• Since \(2\) is the first natural number greater than \(1\) to satisfy this condition, it is the smallest prime number.

• Notably, \(2\) is also the only even prime number in the entire set of real numbers, as all other even numbers are divisible by \(2\).


Step 4: Final Answer:
The smallest prime number is \(2\), making Option (B) the correct choice.