Math & Algebra Tool

Prime Number Checker

Instantly check if any number is prime or composite.

Σ The Formula

Prime if divisible only by 1 and itself | Composite if has other factors

Real World Examples

Prime Example
97 is prime (only divisible by 1 and 97)
Composite Example
12 is composite (factors: 1, 2, 3, 4, 6, 12)
Small Prime
2 is the only even prime number
Large Prime
101 is prime (no factors between 1 and 101)

# About This Calculator

A Prime Number is a natural number greater than 1 that has exactly two distinct factors: 1 and itself. Examples include 2, 3, 5, 7, 11, 13, 17, 19, 23, and so on. Prime numbers are the "building blocks" of all natural numbers through prime factorization.

Primes are fundamental in mathematics, cryptography (RSA encryption), computer science (hash functions), and number theory. They have fascinated mathematicians for millennia - Euclid proved there are infinitely many primes around 300 BC, yet we still discover new patterns and properties today.

A Composite Number has more than two factors. For example, 12 has factors 1, 2, 3, 4, 6, and 12. The number 1 is special - it's neither prime nor composite. The number 2 is the only even prime; all other even numbers are composite (divisible by 2).

This tool instantly checks if any number is prime or composite and shows prime factorization for composite numbers. Perfect for homework, cryptography studies, or exploring number theory patterns.

How To Use

  1. Enter a positive whole number (e.g., 97).
  2. Click Check Prime.
  3. The result will tell you if it's prime or composite.

Frequently Asked Questions

Is 1 a prime number?+

No, 1 is not a prime number because it only has one factor (itself), not two. By definition, primes must have exactly two distinct factors. The number 1 is neither prime nor composite - it's a special case called a unit.

What is the only even prime number?+

2 is the only even prime number. All other even numbers are divisible by 2 (in addition to 1 and themselves), making them composite. This makes 2 unique among primes.

How are prime numbers used in cryptography?+

RSA encryption uses very large prime numbers (hundreds of digits). It's easy to multiply two large primes, but extremely hard to factor the result back into primes. This one-way difficulty secures online banking, messaging, and internet security.

What's the largest known prime number?+

As of 2024, the largest known prime has over 24 million digits! It's a Mersenne prime (form 2^p - 1). The Great Internet Mersenne Prime Search (GIMPS) project continues discovering new record primes using distributed computing.

How can I quickly check if a number is prime?+

Check if it's divisible by any prime up to its square root. For 97: √97 ≈ 9.8, so test primes 2, 3, 5, 7. Since none divide 97, it's prime. This calculator does this instantly for any number!

Is Prime Number Checker free to use?+

Yes, Prime Number Checker on Matheric is completely free to use. We believe in accessible education and utility for everyone.

About

A Prime Number is a natural number greater than 1 that has exactly two distinct factors: 1 and itself. Examples include 2, 3, 5, 7, 11, 13, 17, 19, 23, and so on. Prime numbers are the "building blocks" of all natural numbers through prime factorization.

Primes are fundamental in mathematics, cryptography (RSA encryption), computer science (hash functions), and number theory. They have fascinated mathematicians for millennia - Euclid proved there are infinitely many primes around 300 BC, yet we still discover new patterns and properties today.

A Composite Number has more than two factors. For example, 12 has factors 1, 2, 3, 4, 6, and 12. The number 1 is special - it's neither prime nor composite. The number 2 is the only even prime; all other even numbers are composite (divisible by 2).

This tool instantly checks if any number is prime or composite and shows prime factorization for composite numbers. Perfect for homework, cryptography studies, or exploring number theory patterns.

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