Prime Number Checker
Free online prime number checker. No sign-up, no installation. Runs entirely in your browser.
Enter a positive integer. Numbers above 1012 may take longer to process.
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.
For example, 2, 3, 5, 7, 11, and 13 are prime numbers. Prime numbers are fundamental building blocks in mathematics
and cryptography.
How to Use This Tool
- Enter any positive integer in the input field.
- Click the “Check Prime” button.
- The tool will instantly tell you if the number is prime or composite.
- If composite, you’ll see its prime factors and the nearest primes above and below.
- Optionally expand the “View Primes” section to see all primes up to your input value.
Common Use Cases
- Education: Learn about prime numbers and number theory.
- Cryptography: Prime numbers are essential in RSA encryption and security algorithms.
- Mathematics: Verify primality for research, puzzles, or competitions.
- Quick Verification: Check if a number is prime without manual calculations.
Frequently Asked Questions
What is the fastest algorithm to check if a number is prime?
This tool uses trial division up to √n, which is efficient for most numbers.
For very large numbers (> 10¹², use specialized algorithms like Miller-Rabin or AKS primality test).
Is 1 a prime number?
No. By mathematical definition, a prime number must be greater than 1 and have exactly two distinct positive divisors: 1 and itself.
The number 1 only has one divisor, so it is neither prime nor composite.
What’s the difference between prime and composite numbers?
A prime number has exactly two divisors (1 and itself). A composite number has more than two divisors.
For example, 7 is prime, but 12 is composite (divisible by 1, 2, 3, 4, 6, 12).
Can this tool handle very large numbers?
Yes, up to about 10¹⁵ in JavaScript. However, numbers larger than 10¹² may take noticeably longer due to the trial division method.
A warning will appear when you check a very large number.
What are prime factors?
Prime factors are the prime numbers that multiply together to give the original number.
For example, the prime factors of 12 are 2, 2, and 3 (since 2 × 2 × 3 = 12).
Why is 2 the only even prime number?
Because all other even numbers are divisible by 2, they have at least three divisors: 1, 2, and themselves.
This makes them composite. Since 2 is only divisible by 1 and 2 (itself), it is the only even prime.