Prime Number Checker & Prime Factorization
Input & Actions
Tip: accepts integers like 84, -210, or big integers (within reason). Decimals are not supported.
Results will appear here.
Method & Definitions
This tool determines whether a number is prime and computes its prime factorization. It uses optimized trial division up to \( \sqrt{n} \), checking 2, 3, and then only candidates of the form \( 6k \pm 1 \).
- Prime: \(n>1\) with no divisors other than 1 and \(n\).
- Composite: \(n>1\) that is not prime.
- Prime factorization: \( n = \prod p_i^{e_i} \).
\( \text{Prime test: } \nexists d \in \{2,\dots,\lfloor\sqrt{n}\rfloor\} \text{ with } n \bmod d = 0 \)
\( \text{Factorization: } n = \prod p_i^{e_i}, \; e_i \in \mathbb{Z}_{\ge 0} \)
\( \text{Factorization: } n = \prod p_i^{e_i}, \; e_i \in \mathbb{Z}_{\ge 0} \)
FAQ
Is 1 prime?
No. By definition, primes are integers \(\ge 2\).
How are negatives handled?
We display \( -1 \times \) the factorization of \(|n|\). Example: \(-84 = -1 \times 2^2 \times 3 \times 7\).
Performance limits?
Trial division up to \( \sqrt{n} \) is quick for typical classroom sizes (up to ~1010 is usually fine in modern browsers). Extremely large inputs will take longer.