Prime Number Calculator

Understanding Prime Numbers

What is a Prime Number?

A prime number is a natural number greater than 1 that is only divisible by 1 and itself. In other words, it has exactly two factors: 1 and the number itself.

The Concept of Primality

Primality is the property of being prime. To determine if a number is prime, we check if it has any factors other than 1 and itself.

The Formula

There's no simple formula to determine if a number is prime, but we can use the following method:

For a number \(n\), check if it's divisible by any integer from 2 to \(\sqrt{n}\).

If \(n\) is not divisible by any of these numbers, it is prime.

The Process

1. Check if the number is greater than 1
2. If it's 2, it's prime (the only even prime number)
3. If it's even and not 2, it's not prime
4. For odd numbers, check divisibility by odd numbers up to its square root

Example

Let's check if 17 is prime:

1. 17 > 1, continue
2. 17 is odd, continue
3. \(\sqrt{17} \approx 4.12\), so we need to check divisibility by 3
4. 17 ÷ 3 = 5 remainder 2, so 3 doesn't divide 17
5. We've checked all numbers up to \(\sqrt{17}\), and found no divisors
6. Therefore, 17 is prime

Visual Representation

This diagram represents the number 17 as a prime number, isolated and indivisible except by 1 and itself.