The smallest prime number is

A prime number is defined as a natural number greater than 1 that has exactly two distinct positive divisors: 1 and the number itself. By this definition, 1 is excluded from the primes because it has only one divisor (itself).

Applying this definition to 2: its only positive divisors are 1 and 2, so it has exactly two distinct divisors and qualifies as prime. Since 1 — the only natural number smaller than 2 — is excluded from being prime, 2 is the least natural number satisfying the prime definition.

• 3 — divisors 1 and 3, so it is prime, but it is greater than 2 and therefore cannot be the smallest.

• 5 — divisors 1 and 5, so it is prime, but it is greater than 2 and therefore cannot be the smallest.

• 7 — divisors 1 and 7, so it is prime, but it is greater than 2 and therefore cannot be the smallest.

Cross-checking against the standard ascending list of prime numbers — 2, 3, 5, 7, 11, 13, … — confirms 2 as the first term. Hence, the smallest prime number is 2.