🍋 Math Tools
Prime Number Tools
Check, factorize, generate, and find prime numbers
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About Prime Number Tools
Four prime number tools in one: check if a number is prime, find the prime factorization of any number, generate primes up to a limit, or find the Nth prime number.
How It Works
Primality testing uses trial division up to the square root. Factorization uses repeated division by primes. Generation uses the Sieve of Eratosthenes for efficiency. Nth prime uses a counting approach.
Step by Step
- 1 Select an action: check, factorize, generate, or find Nth
- 2 Enter a number in the input area
- 3 Click Calculate to see the result
Tips
- The largest prime you can reliably check is about 10^15
- Every integer greater than 1 has a unique prime factorization
- Generate primes up to 100,000 for fast results
- The 1,000th prime is 7,919
Frequently Asked Questions
Is 1 a prime number?
No. By mathematical convention, 1 is neither prime nor composite. The smallest prime number is 2, which is also the only even prime.
What is the fundamental theorem of arithmetic?
Every integer greater than 1 can be represented uniquely as a product of prime numbers (up to the order of factors). This is why prime factorization is unique.