1. What Are Prime Numbers?

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 The Algorithm Works

The calculator uses trial division algorithm:

Algorithm Steps:

• If number ≤ 1 → NOT PRIME
• If number = 2 → PRIME
• If number is even → NOT PRIME
• Check divisibility by odd numbers up to √n
• If no divisors found → PRIME

3. Trial Division Method

Details: Trial division is the simplest primality test. It checks whether the input number is divisible by any integer between 2 and the square root of the number. This method is efficient for small to medium-sized numbers.

4. Using The Calculator

Tips: Enter any integer between 2 and 1,000,000. The calculator will determine if it's prime using the trial division method. Larger numbers may take longer to compute.

5. Frequently Asked Questions (FAQ)

Q1: What is the largest prime number known?
A: As of 2024, the largest known prime is 2^82,589,933 − 1, a number with 24,862,048 digits.

Q2: Why check only up to √n?
A: If n has a divisor greater than √n, it must have a corresponding divisor less than √n. Checking beyond √n is redundant.

Q3: Are there faster primality tests?
A: Yes, for very large numbers, probabilistic tests like Miller-Rabin or deterministic tests like AKS are more efficient.

Q4: What are prime numbers used for?
A: Prime numbers are fundamental in cryptography (RSA encryption), computer science, and number theory.

Q5: Is 1 a prime number?
A: No, by definition, prime numbers must be greater than 1. This convention simplifies mathematical theorems.