What is a Prime Number?
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. In simpler terms, a prime number can only be divided exactly by 1 and itself.
Key Rules
- 1 is not prime. By definition, a prime number must have exactly two distinct factors: 1 and itself. The number 1 only has one factor.
- 2 is the only even prime. All other even numbers can be divided by 2.
- 0 and negative numbers are not considered prime numbers in standard mathematics.
How do we check?
To check if a large number $N$ is prime, we only need to try dividing it by prime numbers up to the square root of $N$. If we find no divisors in that range, the number is prime.