Prime Number Checker
Check if a number is prime
About This Tool
The Prime Number Checker instantly tells you whether any number is prime. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Enter any number to check if it's prime, find its factors, discover nearby primes, and learn about prime number properties.
How It Works
How to Use This Checker
Checking prime numbers is easy:
- Enter a number - Type any positive integer.
- Click Check - Instantly see if it's prime.
- View details - See factors (if not prime), nearest primes, and more.
- Explore - Generate lists of primes or find prime factors.
Formula
Prime Number Definition
A number n is prime if:
- n > 1
- n has exactly two factors: 1 and n
- n is not divisible by any number from 2 to sqrt(n)
First 20 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71
Examples
Examples
Example 1: Prime Number
- Input: 17
- Result: Prime
- Factors: 1, 17
- Nearest primes: 13, 19
Example 2: Composite Number
- Input: 24
- Result: Not Prime
- Factors: 1, 2, 3, 4, 6, 8, 12, 24
- Prime factorization: 2 cubed x 3
Example 3: Large Prime
- Input: 997
- Result: Prime
- It's the largest 3-digit prime
Frequently Asked Questions
How does the Prime Checker determine if a number is prime?
A prime number is divisible only by 1 and itself. The checker tests divisibility by all primes up to √n. For example, to check if 97 is prime, it only needs to test divisors up to √97 ≈ 9.8, checking 2, 3, 5, and 7.
What is the largest prime number known?
The largest known prime is a Mersenne prime (2^p - 1). As of recent records, it has over 24 million digits. The calculator efficiently checks numbers up to 15 digits using optimized trial division and Miller-Rabin primality testing.
Why are prime numbers important in cryptography?
RSA encryption relies on the difficulty of factoring the product of two large primes. Multiplying two 300-digit primes is fast, but factoring the 600-digit result is computationally infeasible with current technology.
What are twin primes?
Twin primes are pairs of primes that differ by 2: (3,5), (5,7), (11,13), (17,19), (29,31). The twin prime conjecture states there are infinitely many such pairs, but this remains unproven.
Is 1 a prime number?
No. By modern convention, 1 is neither prime nor composite. This definition ensures the fundamental theorem of arithmetic works: every integer greater than 1 has a unique prime factorization. Including 1 would break this uniqueness.
Disclaimer
Disclaimer: This calculator provides results for general reference and educational purposes only. While we strive for accuracy, results for very large numbers may be subject to computational limitations. All processing happens in your browser.
💡 Tips
Tips
- 2 is the only even prime number
- 1 is not considered prime
- All primes greater than 2 are odd
- Check divisibility up to sqrt(n) for efficiency
- Prime numbers are infinite