Prime Checker
Enter a number to determine if it is prime and see its factorization.
How to use the Prime Number Checker
A prime number is divisible only by 1 and itself. This tool tells you instantly whether any positive integer is prime and shows its complete prime factorization.
- 1
Enter a positive integer
Type any whole number greater than zero into the Number field. The tool works for small numbers (2, 3, 7) and large numbers alike.
- 2
Click Check
The tool tests whether the number is prime and computes its prime factorization using trial division up to the square root of the number.
- 3
Read the result
The result card shows whether the number is prime or not prime, followed by its list of prime factors expressed as a multiplication (e.g.
60 = 2 × 2 × 3 × 5).
Frequently asked questions
What is a prime number?
A prime number is an integer greater than 1 that has no positive divisors other than 1 and itself. The first several primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. The number 2 is the only even prime.
What is the largest known prime?
As of 2024, the largest known prime is 282,589,933 − 1, a Mersenne prime with more than 24 million digits. It was discovered in 2018 using distributed computing in the Great Internet Mersenne Prime Search (GIMPS) project.
How does primality testing work?
For small to medium numbers, trial division checks divisibility by all integers up to the square root of the candidate. If none divide evenly, the number is prime. For very large numbers, probabilistic tests like Miller-Rabin are used because trial division becomes too slow.
What is prime factorization?
Every composite (non-prime) number can be expressed as a product of prime numbers: 60 = 2 × 2 × 3 × 5. This decomposition is unique (the Fundamental Theorem of Arithmetic). Prime factorization is used in computing GCD/LCM, cryptography (RSA), and number theory.
Are 0 and 1 prime numbers?
No. By definition, prime numbers must be greater than 1. The number 1 is called a "unit" — it is neither prime nor composite. Zero is not a natural number in the standard definition and is also not prime.
Where are prime numbers used in computing?
Primes are fundamental to public-key cryptography (RSA, Diffie-Hellman), hash table sizing, pseudo-random number generation, digital signatures, and error-correcting codes. The security of modern internet encryption depends on the difficulty of factoring large primes.