Prime Number Checker
Check if any number is prime, find its prime factorization, get all divisors, and generate lists of prime numbers. Features previous/next prime lookup and ordinal position (e.g., '97 is the 25th prime').
Embed This Tool
Add this tool to your website with customizable styling
How to Use
- 1 Choose your mode — Select "Check Number" to test a single number, or "Generate Primes" to create a list of prime numbers.
- 2 Enter a number — In Check mode, type any positive integer. In Generate mode, enter a count or range.
- 3 Click the action button — Press "Check if Prime" or "Generate" to perform the calculation.
- 4 View the results — See whether the number is prime, its factorization if composite, previous/next primes, and ordinal position.
- 5 Copy or explore — Copy results to clipboard or use the generated prime list for further analysis.
💡 Pro Tip: For non-prime numbers, the tool shows the prime factorization in both exponential form (2² × 5²) and expanded form (2 × 2 × 5 × 5).
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. The number 2 is the only even prime number.
How do I check if a number is prime?
Enter any positive integer and click "Check if Prime". The tool will instantly tell you whether the number is prime or not. For non-prime numbers, it shows the complete prime factorization (e.g., 100 = 2² × 5²) and all divisors.
What is prime factorization?
Prime factorization breaks down a number into the product of prime numbers. For example, 60 = 2² × 3 × 5. Every positive integer greater than 1 has a unique prime factorization (Fundamental Theorem of Arithmetic).
How can I generate a list of prime numbers?
Switch to "Generate Primes" mode. You can either generate the first N primes (e.g., first 100 primes) or all primes within a specific range (e.g., primes between 1 and 1000). The tool uses an efficient algorithm to find primes quickly.
What is the largest prime number I can check?
This tool efficiently handles numbers up to 10 million. For very large numbers, the primality test uses optimized trial division checking only up to the square root.