Prime Number Calculator

How to use

1. 1Type any whole number up to eighteen digits into the input. Underscores and spaces between digits are allowed (1_000_000 or 1 000 000).
2. 2Read the verdict at the top: prime, composite, or neither (for 0 and 1).
3. 3Check the prime factorization in exponent form (for example 360 = 2^3 * 3^2 * 5) and the expanded multiplication, with copy buttons for both.
4. 4Review the divisor stats panel for the number of divisors (tau), the sum of divisors (sigma), and the full sorted list of divisors.
5. 5Use the next and previous prime cards, including the Use this number buttons, to step through primes around your value, or copy the full plain-text report.

About this tool

Prime Number Calculator answers four questions about any whole number up to eighteen digits at once: is it prime, what are its prime factors, what are all of its divisors, and what is the closest prime above and below it. The primality test runs deterministic Miller-Rabin against the small-prime witness set 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, which is provably correct for every input the tool accepts. Prime factorization combines trial division for small factors with Brent's variant of Pollard's rho for larger composite cofactors, so values like 1234567 or 999999937 resolve in milliseconds without sending anything off-device. Beyond the verdict, the tool reports the factorization in exponent form (so 360 reads as 2^3 * 3^2 * 5), the expanded multiplication, the count of distinct prime factors, the total prime factors with multiplicity, the full sorted list of divisors, the divisor count (the tau function), the divisor sum (the sigma function), the next prime after the input, and the largest prime smaller than the input. Quick presets cover textbook examples (97, 360, 1024, 9973, 100000, 1234567, 999999937), and the next and previous prime cards include Use this number buttons so you can step through primes without retyping. Useful for math homework on primes and divisibility, programming exercises that involve sieves or factor counting, cryptography classroom work where Miller-Rabin and Pollard's rho are the textbook examples, and quick sanity checks when you just need to know whether a number is prime. Everything runs locally on your device using BigInt, so the numbers you enter for assignments, exam practice, or research stay in your browser.

Free to use. Works in your browser. No signup, no login.