Prime Calculator | Interactive Mathematics Tools

What is a Prime Number?

A prime number is a natural number greater than 1 that is only divisible by 1 and itself. Examples include 2, 3, 5, 7, 11, and 13.

Example: Is 17 Prime?

17 can only be divided by 1 and 17.

Result: 17 is a prime number.

What is a Composite Number?

A composite number is a natural number greater than 1 that has factors other than 1 and itself. Examples include 4, 6, 8, 9, and 10.

Example: Is 24 Composite?

24 can be divided by 1, 2, 3, 4, 6, 8, 12, and 24.

Result: 24 is a composite number.

Methods to Check Prime Numbers

Trial Division Method

The most basic method to check if a number is prime:

Divide the number by each integer from 2 to its square root
If any number divides evenly, it's composite
If no numbers divide evenly, it's prime

function isPrime(n) {
    if (n <= 1) return false;
    for (let i = 2; i <= Math.sqrt(n); i++) {
        if (n % i === 0) return false;
    }
    return true;
}

Sieve of Eratosthenes

An efficient method to find all prime numbers up to a given limit:

Create a list of numbers from 2 to n
Start with the first prime number (2)
Mark all its multiples as composite
Move to the next unmarked number and repeat

Historical Timeline

Ancient Greece (300 BC)

Euclid proves there are infinitely many prime numbers in his work "Elements"

Middle Ages

Arab mathematicians develop advanced methods for finding prime numbers

17th Century

Fermat introduces important theorems about prime numbers

Modern Era

Prime numbers become crucial in computer security and cryptography

Properties of Prime Numbers

Fundamental Properties

Every number greater than 1 is either prime or composite
2 is the only even prime number
There are infinitely many prime numbers
Prime numbers become less frequent as numbers get larger

Special Types of Primes

Twin Primes: Pairs of primes that differ by 2 (e.g., 3 and 5)
Mersenne Primes: Primes of the form 2n-1
Sophie Germain Primes: Where p and 2p+1 are both prime

Practical Applications

Cryptography

Prime numbers are fundamental to modern encryption methods, especially in:

RSA encryption
Digital signatures
Secure communications

Computer Science

Prime numbers are used in:

Hash functions
Random number generation
Error correction codes

Common Questions

Why is 1 not prime?

1 is neither prime nor composite because it has only one factor (itself). Prime numbers must have exactly two factors.

Largest Known Prime

The largest known prime number is constantly changing as larger ones are discovered. Most recent discoveries are Mersenne primes.

Fun Fact

The ancient Greeks proved that there are infinitely many prime numbers using a simple but clever proof: If you assume there are finitely many primes, you can always construct a new one, contradicting the assumption.

Reference Table

Range	Number of Primes	Example Primes
1-10	4	2, 3, 5, 7
11-20	4	11, 13, 17, 19
21-30	2	23, 29

Prime Number Calculator