What prime number checker algorithm does this use?

It uses exact trial division up to the integer square root. Small candidates come from a bundled prime list; larger candidates follow 6k - 1 and 6k + 1 after 2 and 3 have been ruled out. A divisor proves that a number is composite. If the search reaches the square root without finding one, the number is prime. For example, 49 is composite because 7 × 7 = 49.

Are 0 and 1 prime numbers?

Neither 0 nor 1 is prime or composite. A prime is a whole number greater than 1 with exactly two positive divisors: 1 and itself. The tool reports neither for 0 and 1.

What is the largest number it will check?

The largest accepted number is 1,000,000,000,000. The ceiling bounds the time spent on exact trial division, whose search grows with the square root. Larger inputs are refused with a message naming the limit.

How is this different from a probabilistic prime test?

Some primality tests return a probable-prime result from selected witnesses; fixed witness sets can also provide deterministic results within a stated range. This checker instead uses exact trial division within its stated ceiling. It shows a divisor for a composite or exhausts the candidate range for a prime.

How long does a check take, and what does Stop do?

Numbers with a small factor are usually settled as you type. When the fixed initial division budget is exhausted, Check continues in a background worker and shows its progress. Stop ends that worker. Completion time depends on the number and device.

What happens with a decimal, a negative number or a typo?

Decimals, negative numbers and letters are refused with a message naming the problem. Thousands separators must group in threes: 600,851,475,143 is accepted, while 1,5 is refused. Inputs are never rounded to an integer.

Is my number uploaded, and what does All factors show?

The arithmetic runs in this browser. The number is remembered locally. All factors lists the smallest 200 positive divisors in order and shows the total divisor count when there are more. Copy puts the verdict and its evidence on the clipboard.

Prime Number Checker

Check whether a whole number up to 1,000,000,000,000 is prime, composite or neither. A composite result shows its smallest factor and factor pair. Choose All factors to list divisors, or copy the verdict. Longer checks run in a background worker with a Stop button.

600,851,475,143Compositesmallest factor 71 · 600,851,475,143 = 71 × 8,462,696,833

stopped at 71

Number

Show

600,851,475,143 is composite. Its smallest factor is 71, and 600,851,475,143 = 71 × 8,462,696,833.

Whole numbers from 0 up to 1,000,000,000,000. Thousands may be grouped in threes, as 600,851,475,143.

2the only even prime
prime
1no factors above itself
neither prime nor composite
497 × 7
composite, smallest factor 7
4.5not a whole number
4.5 is not a whole number. Prime and composite describe whole numbers only, and this will not round one for you: drop the part after the point.

Proved, not guessed, up to a stated limit. A composite number always has a factor at or below its own square root, so dividing by every candidate up to that point and finding none is a proof that the number is prime, not a strong suspicion. That is the whole method here: 2, then 3, then every number of the form 6k - 1 and 6k + 1, which is every candidate that 2 and 3 have not already ruled out. Numbers are tested by dividing by every candidate up to the square root, so a prime result is a proof and a composite result comes with the factor that settles it. That is exact up to 1,000,000,000,000. Larger numbers are refused rather than answered with a probabilistic test. A number that needs the long scan runs in a background worker, so the page keeps responding and Stop ends the work.

Common questions

What prime number checker algorithm does this use?: It uses exact trial division up to the integer square root. Small candidates come from a bundled prime list; larger candidates follow 6k - 1 and 6k + 1 after 2 and 3 have been ruled out. A divisor proves that a number is composite. If the search reaches the square root without finding one, the number is prime. For example, 49 is composite because 7 × 7 = 49.
Are 0 and 1 prime numbers?: Neither 0 nor 1 is prime or composite. A prime is a whole number greater than 1 with exactly two positive divisors: 1 and itself. The tool reports neither for 0 and 1.
What is the largest number it will check?: The largest accepted number is 1,000,000,000,000. The ceiling bounds the time spent on exact trial division, whose search grows with the square root. Larger inputs are refused with a message naming the limit.
How is this different from a probabilistic prime test?: Some primality tests return a probable-prime result from selected witnesses; fixed witness sets can also provide deterministic results within a stated range. This checker instead uses exact trial division within its stated ceiling. It shows a divisor for a composite or exhausts the candidate range for a prime.
How long does a check take, and what does Stop do?: Numbers with a small factor are usually settled as you type. When the fixed initial division budget is exhausted, Check continues in a background worker and shows its progress. Stop ends that worker. Completion time depends on the number and device.
What happens with a decimal, a negative number or a typo?: Decimals, negative numbers and letters are refused with a message naming the problem. Thousands separators must group in threes: 600,851,475,143 is accepted, while 1,5 is refused. Inputs are never rounded to an integer.
Is my number uploaded, and what does All factors show?: The arithmetic runs in this browser. The number is remembered locally. All factors lists the smallest 200 positive divisors in order and shows the total divisor count when there are more. Copy puts the verdict and its evidence on the clipboard.

Numbers are tested by dividing by every candidate up to the square root, so a prime result is a proof and a composite result comes with the factor that settles it. That is exact up to 1,000,000,000,000. Larger numbers are refused rather than answered with a probabilistic test.