What is a prime number?

A prime number is a positive integer greater than 1 that has exactly two divisors: itself and 1. Examples are 2, 3, 5, 7, and 11. The number 2 is the only even prime.

No. By definition, a prime must have exactly two distinct positive divisors. The number 1 has only one divisor (itself), so it is neither prime nor composite.

How can I check if a number is prime quickly?

Test divisibility by all primes up to the square root of the number. If none divide it evenly, it is prime. For example, to check 97, test divisibility by 2, 3, 5, and 7 only, since 11² exceeds 97.

What are prime factors?

Prime factors are the prime numbers that multiply together to produce the original number. For example, the prime factorization of 84 is 2 × 2 × 3 × 7 = 2² × 3 × 7.

Why do prime numbers matter in computing?

Large primes are fundamental to modern cryptography. RSA encryption, which secures much of the internet, relies on the fact that multiplying two large primes is easy but factoring their product is extremely hard.

Prime Number Checker

Find out instantly whether a number is prime. The prime number checker tests any positive integer and, if it is not prime, returns its prime factorization.

Number

How to Use the Prime Number Checker

Enter a positive integer.
Click Check to see whether it is prime.
For composite numbers, review the prime factorization and divisor count.

How It Works

The checker tests divisibility by all primes up to the square root of the number, using the 6k±1 optimization. A number with exactly two divisors (itself and 1) is prime; 1 is neither prime nor composite.

Frequently asked questions

Everything you need to know about this calculator.

Math

LCM & GCD Calculator

Free LCM and GCD calculator. Enter two or more numbers to find their least common multiple and greatest common divisor instantly.

Open

Tools

Random Number Generator

Free random number generator. Generate one or many random numbers within any range, with optional uniqueness and decimal support.

Open

Tools

Probability Calculator

Free probability calculator for single, multiple, and conditional events. Find the chance of independent and dependent outcomes quickly.

Open

Math

Average Calculator

Free average calculator. Enter any number of values to instantly compute the mean, median, and mode of your data set.

Open

How to Use the Prime Number Checker

How It Works

Frequently asked questions

What is a prime number?

Is 1 a prime number?

How can I check if a number is prime quickly?

What are prime factors?

Why do prime numbers matter in computing?

Related Calculators

LCM & GCD Calculator

Random Number Generator

Probability Calculator

Average Calculator