A prime input
104729 is prime: no integer from 2 through its square-root bound divides it evenly.
Calculations run locally in your browser. This tool does not upload the numbers you enter.
How to use the Prime Number Checker
- 01
Enter a whole integer from 0 through 1,000,000,000,000 without commas or scientific notation.
- 02
Select Calculate to run the exact check. A composite result includes a factor pair.
- 03
Load the example to check 104729, clear the input to start again, or copy and download your result.
Examples
A composite input
221 is composite. Its smallest prime divisor is 13, and 13 × 17 = 221.
Why the square root is enough
If a positive integer has a nontrivial factor pair, at least one of the factors cannot exceed its square root. The checker tests 2 and 3 first, then possible divisors of the forms 6k − 1 and 6k + 1. It stops at the first divisor or when the divisor squared exceeds the input.
Prime, composite, or neither
A prime is an integer greater than 1 with no positive divisors other than 1 and itself. Composite integers have another divisor. Zero and one are neither prime nor composite; they are reported separately rather than being mislabeled as composite.
An exact bounded check
The input and divisibility operations use JavaScript BigInt, avoiding floating-point rounding of integers. The upper bound limits the trial-division work in your browser. This tool does not make probabilistic guesses or claim to test cryptographic-size candidates.
What to know
- Exact integer input is limited to 0–1,000,000,000,000.
Common questions
Why is 2 prime?
Two has exactly two positive divisors, 1 and 2. It is also the only even prime.
Can I enter a negative number?
This checker uses the usual positive-integer definition and accepts zero through one trillion. Negative integers are outside its input range.
Why reject numbers larger than one trillion?
Trial division becomes slow for large prime candidates. The stated bound keeps a worst-case check limited to divisors below one million.
Can I use the result for cryptographic key generation?
No. This is an educational integer checker with a small bound, not a cryptographic prime generator.