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A prime number is a whole number greater than 1 that has no divisors other than 1 and itself. This checker uses trial division — testing potential divisors up to the square root of the number — the standard efficient method for checking primality by hand or by computer.
If the number isn't prime, it also reports the smallest factor found.
How it works
Enter any whole number. The calculator tests divisibility by every integer from 2 up to the square root of the number — if none divide evenly, the number is prime.
- Enter number.
- Click Calculate to see your results.
Examples
Checking a well-known prime
97 is prime — no whole number from 2 to 9 (its square root, rounded down) divides evenly into it.
Who should use it
- Number theory and math homework.
- Quickly verifying whether a number is prime before using it in another calculation (like cryptography examples).
Industry applications
- Mathematics education
- Computer science and cryptography fundamentals
Advantages
- Uses the efficient square-root trial division method rather than checking every number up to n.
- Reports the smallest factor found for composite numbers.
Limitations
- For extremely large numbers (many digits), trial division becomes slow — specialized algorithms are used in cryptography instead.
Common mistakes to avoid
- Testing divisors well beyond the square root, which wastes effort — nothing new can be found past that point.
- Assuming a large number is automatically prime just because it's not divisible by small numbers like 2, 3, or 5.
Best practices
- When checking by hand, test 2 first, then only odd numbers afterward — no even number greater than 2 can be prime.
Tips
- Every prime number greater than 3 is either one more or one less than a multiple of 6 — a quick (though not definitive) sanity check.