1. What is Prime and Composite Number?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A composite number is a natural number greater than 1 that is not prime, meaning it has divisors other than 1 and itself.

2. How Does the Calculator Work?

The calculator checks if a number is prime by testing divisibility:

Algorithm:

• If n ≤ 1: Not prime (invalid input)
• If n = 2: Prime
• If n is even and > 2: Composite
• Check odd divisors from 3 to √n
• If any divisor found: Composite
• Otherwise: 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 of many encryption algorithms used in secure communications.

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, specialized algorithms may be more efficient.

5. Frequently Asked Questions (FAQ)

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

Q2: What is the smallest prime number?
A: 2 is the smallest and only even prime number.

Q3: Are there infinitely many prime numbers?
A: Yes, this was proven by Euclid around 300 BC.

Q4: What are prime numbers used for?
A: Prime numbers are essential in cryptography, particularly in RSA encryption, hash functions, and various security protocols.

Q5: How are large prime numbers found?
A: Specialized algorithms like the Sieve of Eratosthenes, Miller-Rabin test, and Lucas-Lehmer test are used to find and verify large primes.