1. What Is Prime Number?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Prime numbers are the building blocks of all natural numbers through multiplication.

2. How To Calculate Prime Numbers?

The algorithm checks divisibility up to the square root of the number:

Algorithm Steps:

• Check if number is less than 2 → not prime
• Check if number equals 2 → prime
• Check if number is even → not prime (except 2)
• Check odd divisors from 3 to √n
• If no divisors found → prime

Explanation: This method efficiently determines primality by reducing the number of checks needed.

3. Importance Of Prime Numbers

Details: Prime numbers are fundamental in mathematics and computer science, used in cryptography, number theory, and as the basis for many mathematical proofs and algorithms.

4. Using The Calculator

Tips: Enter any integer greater than 1. The calculator will determine if it's prime or composite. For very large numbers, calculation may take longer.

5. Frequently Asked Questions (FAQ)

Q1: Is 1 a prime number?
A: No, by definition prime numbers must be greater than 1. The smallest prime number is 2.

Q2: What are the first few prime numbers?
A: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, etc.

Q3: Why check only up to √n?
A: If n has a divisor greater than √n, it must have a corresponding divisor less than √n, so checking beyond √n is redundant.

Q4: Are there infinitely many prime numbers?
A: Yes, this was proven by Euclid over 2000 years ago. There is no largest prime number.

Q5: What are prime numbers used for?
A: Cryptography (RSA encryption), hash tables, random number generation, and as fundamental elements in number theory.