Prime Number Calculator
Enter a number to check whether it's prime, see all its factors, or generate a list of prime numbers up to a limit you choose.
Prime Number Calculator
Check primality, factors and prime lists
A prime number is a whole number greater than 1 that has exactly two factors: 1 and itself. The calculator tests divisibility up to the square root of the number.
What Makes a Number Prime?
A prime number is a whole number greater than 1 whose only factors are 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
**How the check works**: To test whether n is prime, the calculator tries dividing n by every whole number from 2 up to √n. If any division comes out even, n is composite. If none do, n is prime. This works because if n had a factor larger than √n, its matching factor would be smaller than √n.
**Prime factorization**: Every whole number greater than 1 can be written uniquely as a product of primes (the Fundamental Theorem of Arithmetic).
- Prime = only factors are 1 and itself
- 2 is the only even prime
- Test divisors up to √n
- Unique prime factorization
Worked Example
Example: Is 29 prime?
- √29 ≈ 5.39, so test divisors 2, 3, 4, 5 - 29 ÷ 2 = 14.5 (not even) - 29 ÷ 3 = 9.67 (not even) - 29 ÷ 4 = 7.25 (not even) - 29 ÷ 5 = 5.8 (not even) - No divisors found → 29 is prime
Example: Is 36 prime? - 36 ÷ 2 = 18 (even) → composite - Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 - Prime factorization: 2 × 2 × 3 × 3 = 2² × 3²
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Open calculator →Frequently Asked Questions
Is 1 prime?
No. By definition, a prime number must be greater than 1. 1 is neither prime nor composite.
What's the largest prime?
There is no largest prime — primes go on forever (proved by Euclid). This calculator handles numbers up to about 100 billion accurately.
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