Prime Number Checker

How to use Prime Number Checker

1. Type a whole number up to 9,007,199,254,740,992 (2^53) and press Check.
2. Read whether it is prime or composite, its smallest prime factor and its prime factorisation.
3. To list primes, enter a limit up to 1,000,000 and press List primes.
4. Copy the list if you need it elsewhere.

Understanding primes

Every whole number greater than 1 is either prime or can be written in exactly one way as a product of primes. This is the fundamental theorem of arithmetic, and it is why prime factorisation is so useful: it lets you find greatest common divisors, least common multiples and simplified fractions.

Examples: 97 has no divisor up to its square root (9.8), so it is prime. 91 is composite because 91 = 7 × 13. 360 = 2^3 × 3^2 × 5.

How the methods work

To test a single number n, the checker only needs to look for divisors up to the square root of n, because a larger divisor would pair with a smaller one. For a number near 2^53 that means checking roughly thirty million candidates, which takes a fraction of a second to a few seconds depending on your device.

To list primes the tool uses the sieve of Eratosthenes: it marks the multiples of each prime as composite and keeps what is left. There are 25 primes up to 100 and 78,498 primes up to 1,000,000.

• Use it to check homework and number-theory exercises.
• Pick numbers for hash table sizes or examples in programming.
• Factorise numbers to simplify fractions or find common divisors.

Limits

The tool does not do cryptographic-size primality testing. Inputs larger than 2^53 are rejected. The list is capped at one million to keep the page responsive. Commas and spaces in the input are ignored. Everything runs locally.

Why use this prime number checker tool

• Exact up to 2^53. Numbers in this range are represented exactly by the browser, so the answer is reliable.
• Prime factorisation. Composite numbers are broken into prime powers such as 2^3 × 3^2 × 5.
• Prime list. A sieve of Eratosthenes lists every prime up to your limit and counts them.
• Fast and local. Trial division by numbers of the form 6k±1 runs on your device with no uploads.

Frequently asked questions

More free tools