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Prime Number Checker: Is My Number Prime?

This free prime number checker tells you whether a whole number is prime. If it is not, you get the smallest factor, the full prime factorization, and the nearest primes on either side.

By Debmedia Technologies LLP · Kolkata, India · Updated

What Is It and When Do You Need It?

A prime number cannot be split into smaller whole-number factors. Primes are the building blocks of every whole number, and they power modern encryption. Many people just want a fast answer to is this number prime? for school work or puzzles.

This tool answers that, and for composite numbers it also gives the complete prime factorization, the number of divisors and the closest primes below and above.

How to Use This Tool

  1. Type a whole number from 2 to 100,000,000,000,000.
  2. Press Calculate.
  3. Read whether it is prime or composite.
  4. Open the table for the factors, divisor count and neighboring primes.

How the Calculation Works

The tool uses trial division. A number n is prime if no whole number from 2 up to the square root of n divides it. Only 2 and odd numbers need testing, which makes checks fast.

For a composite number the same loop collects the factors one by one, which gives the prime factorization. The divisor count comes from the exponents: if n = p^a × q^b, there are (a + 1)(b + 1) divisors.

Worked Example

Test 360. It is composite, with prime factorization 2³ × 3² × 5. The divisor count is (3 + 1)(2 + 1)(1 + 1) = 24. The nearest primes are 359 below and 367 above. Test 97 and the answer is prime, with 89 before it and 101 after it.

Common Uses

  • Homework on factors and primes.
  • Finding the right modulus for hashing or random number code.
  • Number puzzles and coding challenges.
  • Simplifying fractions through factorization.

Tips and Common Mistakes

  • Every even number above 2 is composite.
  • A number ending in 5 above 5 is divisible by 5.
  • Use the GCD tool to find shared factors between two numbers.

Next, you may need the GCD and LCM calculator, Fibonacci calculator, permutation and combination calculator, fraction calculator.

Everything runs in your browser. Nothing you type is uploaded, stored or sent to any outside service.

Frequently Asked Questions

A prime number is a whole number greater than 1 that has exactly two divisors: 1 and itself. The first primes are 2, 3, 5, 7, 11 and 13.
No. It has only one divisor, itself, so it does not meet the two-divisor rule. Zero and negative numbers are not prime either.
Yes. It is the only even prime, because every other even number is divisible by 2.
The tool tests numbers up to 100 trillion (10^14) quickly. Larger numbers need special algorithms and are not supported.

Disclaimer: results are calculated in your browser from the numbers you enter. Check important results before you rely on them for money, health, safety or legal decisions.