Question 1

What is a prime number?

Accepted Answer

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first primes are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

Question 2

Is 1 a prime number?

Accepted Answer

No. 1 is not prime. By the modern definition a prime must be greater than 1 and have exactly two distinct positive divisors: 1 and itself. 1 has only one divisor, so it is neither prime nor composite.

Question 3

What is prime factorization?

Accepted Answer

Every integer greater than 1 can be written as a unique product of prime numbers. For example 360 = 2³ × 3² × 5. The factorization uses trial division and a deterministic Miller-Rabin check for large factors.

Question 4

How fast is the primality test?

Accepted Answer

The single-number check uses trial division with a 6k±1 wheel plus a deterministic Miller-Rabin for numbers above 3.3 million, so 18-digit numbers finish in under a millisecond on a typical laptop.