Prime identification — Which is the first (smallest) prime number according to the standard definition of primes?

Introduction / Context:Understanding the definition of a prime number is foundational. A prime is an integer greater than 1 that has exactly two distinct positive divisors: 1 and the number itself. This simple definition immediately identifies the smallest prime and avoids common misconceptions found in early number theory questions.

Given Data / Assumptions:

• A prime must be greater than 1.
• It must have exactly two distinct positive divisors.
• We are to choose the smallest number fulfilling these conditions.

Concept / Approach:Check the candidates in increasing order: 0, 1, 2, 3, 5. Values 0 and 1 do not satisfy the prime definition. The number 2 is divisible only by 1 and 2, and is thus the smallest prime. The next prime is 3; however, the question asks for the first prime only, which is 2.

Step-by-Step Solution:Evaluate 0: has infinitely many divisors; not prime.Evaluate 1: has only one positive divisor (1); not prime.Evaluate 2: divisors are 1 and 2; prime.Therefore the first prime is 2.

Verification / Alternative check:List small primes: 2, 3, 5, 7, 11. The smallest is 2, confirming the choice.

Why Other Options Are Wrong:

• 0 and 1: Do not meet prime criteria.
• 3 and 5: These are primes, but not the first; they are larger than 2.

Common Pitfalls:Thinking 1 is prime; forgetting that 2 is the only even prime; confusing definitions that apply to composites and primes.

Final Answer:2