Boneyard Tools

Prime Number Checker

Type a whole number and the checker instantly tells you whether it is PRIME or NOT PRIME. Composite numbers also show their prime factorization in tidy exponent form, and every number lists its complete set of divisors as tappable chips. The maths runs in your browser, so answers appear the moment you change the value.

How to check a prime number

  1. Type a whole number from 1 to 1,000,000 into the 'Number to check' box.
  2. Read the green PRIME or amber NOT PRIME badge at the top of the result.
  3. For a composite number, read the prime factorization line, for example 360 = 2^3 x 3^2 x 5.
  4. Scan the divisor chips below to see every number that divides yours evenly.
  5. Change the value to check another number, with results updating as you type.

Examples

A prime number

97
PRIME. Divisors (2): 1 and 97, with no factorization line.

A composite number

360
NOT PRIME. 360 = 2^3 x 3^2 x 5, with 24 divisors listed.

A perfect square

100
NOT PRIME. 100 = 2^2 x 5^2, Divisors (9): 1, 2, 4, 5, 10, 20, 25, 50, 100.

Frequently asked questions

What is a prime number?

A prime number is a whole number greater than 1 whose only positive divisors are 1 and itself. The first primes are 2, 3, 5, 7, 11 and 13, and 2 is the only even prime because every other even number is divisible by 2.

Why is 1 not prime?

A prime must have exactly two distinct divisors, namely 1 and itself. The number 1 has just one divisor, so it fails that test and is classed as neither prime nor composite. The tool shows that message and lists a single divisor for it.

How does it read the factorization line?

The factorization is the number written as a product of primes, grouped into exponent form. A prime that appears once is shown bare, so 360 = 2^3 x 3^2 x 5 means three 2s, two 3s and one 5 multiplied together. Prime numbers show no factorization line because their only factor is themselves.

What does the divisor list include?

It lists every positive whole number that divides yours with no remainder, in ascending order, always starting with 1 and ending with the number itself. A prime shows exactly two chips, while a highly composite number like 360 shows 24.

What is prime factorization used for?

Breaking a number into primes is the foundation for finding greatest common divisors and least common multiples, reducing fractions to lowest terms, and the public-key cryptography that protects online traffic. It also reveals structure, such as whether a number is a perfect square.

How large a number can I check here?

The input box accepts whole numbers from 1 to 1,000,000, which covers everyday factoring and homework. The underlying engine and API can factor larger integers exactly, up to the point where JavaScript can still represent them without rounding.

Is the primality test exact or a guess?

It is exact for the supported range. The checker uses trial division, testing divisibility up to the square root of the number, so a true result means the number genuinely has no smaller factors rather than a probabilistic estimate.

What is the largest known prime?

Record primes are gigantic Mersenne primes with tens of millions of digits, discovered by distributed projects such as GIMPS. Those live far beyond this tool, which is built for practical numbers you can read and reason about.

Does the checker keep my numbers private?

Yes. The calculation runs entirely in your browser and nothing you type is sent to a server, so you can use it offline once the page has loaded.

Learn more

  • Prime factorization explained

    What prime factorization means, why every number has exactly one, and how to read the exponent form this checker produces.

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