Prime Number Checker
Check if a number is prime, find its factors, and see its prime factorization.
Free Prime Number Checker
This tool instantly determines whether a number is prime and provides a complete factorization breakdown. It uses an efficient trial division algorithm that checks divisibility up to the square root, making it fast for numbers up to 100 million. You also get a list of all factors and the nearest prime numbers above and below your input.
How to Use
- Enter a positive integer in the input field (up to 100,000,000).
- Click "Check" or press Enter.
- The result will show whether the number is prime (green) or not prime (red).
- If not prime, you will see the prime factorization (e.g., 12 = 2 × 2 × 3).
- All factors and the nearest primes are listed below the result.
Frequently Asked Questions
What is a prime number?
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
Is 1 a prime number?
No. By mathematical convention, 1 is not considered a prime number. The smallest prime is 2, which is also the only even prime.
What is prime factorization?
Prime factorization is the process of expressing a number as a product of prime numbers. For example, 60 = 2 × 2 × 3 × 5. Every integer greater than 1 has a unique prime factorization (Fundamental Theorem of Arithmetic).
How large of a number can I check?
This tool supports numbers up to 100 million (100,000,000). The efficient algorithm checks divisibility only up to the square root, so even large numbers are processed in milliseconds.
What are "nearest primes"?
These are the largest prime smaller than your input and the smallest prime larger than your input. They help you quickly find nearby primes when your number isn't prime itself.