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Prime number checker

Check whether an integer is prime and see a divisor or the exact trial-division evidence.

Exact primality check97 Prime

No integer divisor from 2 through 9. Trial division through √97 proves this result.

Only divisors through ⌊√n⌋ = 9 are needed.

Whole numbers from 0 to 4,294,967,295.

No probabilities: every answer is proven within the stated range.

Processed on your device

How it works & useful details

How it works & limits

A prime is an integer greater than 1 divisible only by itself and 1. Zero and one are neither prime nor composite. Even numbers are checked first, then odd candidates up to the square root.

Checks are exact for integers from 0 to 4,294,967,295. The largest input needs fewer than 33,000 divisions, so this bounded preview stays local and quick. A composite result shows one factor pair, not a complete prime factorization.

Your working space

Change the values to explore the preview. Use the action below to create a copyable, downloadable result. All calculations stay on this device; refreshing clears your work.