1. What is a 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 Does the Prime Checker Work?

The calculator uses the trial division method:

Where:

• \( n \) — The number to check for primality
• \( \sqrt{n} \) — Square root of n (upper bound for checking divisors)

Explanation: The algorithm checks divisibility by all integers from 2 up to the square root of n. If no divisors are found, the number is prime.

3. Importance of Prime Numbers

Details: Prime numbers are fundamental in mathematics and have crucial applications in cryptography, computer science, and number theory. They form the basis for modern encryption algorithms like RSA.

4. Using the Calculator

Tips: Enter any integer greater than 1 to check if it's prime. The calculator will quickly determine whether your number is prime or composite.

5. Frequently Asked Questions (FAQ)

Q1: What is the smallest prime number?
A: The smallest prime number is 2, which is also the only even prime number.

Q2: Are there infinite prime numbers?
A: Yes, Euclid proved over 2000 years ago that there are infinitely many prime numbers.

Q3: What are twin primes?
A: Twin primes are pairs of primes that differ by 2, such as (3,5), (5,7), (11,13).

Q4: Can prime numbers be negative?
A: No, by definition prime numbers are natural numbers greater than 1.

Q5: What is the largest known prime number?
A: The largest known prime numbers are Mersenne primes, discovered through distributed computing projects like GIMPS.