Prime Number Checker
Result
| Is it prime? | ||
|---|---|---|
| Details |
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Prime Number Checker — Instant Verdict, Full Explanation
Is 91 prime? (No — 7 × 13, the classic trap.) Is 997 prime? (Yes — the largest three-digit prime.) This free checker tests any number instantly and, when the answer is composite, shows the smallest factor, complete factor list, and prime factorization — plus the nearest primes in both directions. In-browser, no signup.
The √n Insight That Makes Testing Fast
Factors pair up around the square root: for 100, the pairs are 2×50, 4×25, 5×20, 10×10. If nothing up to √n divides n, no factor exists above it either — so testing 10,007 for primality means trial-dividing by primes up to 100 only, not 10,000 candidates. This single observation makes primality checking practical by hand and instant by machine.
Traps and Landmarks
| Number | Verdict | Why it fools people |
|---|---|---|
| 91 | 7 × 13 | No small obvious factor |
| 57 | 3 × 19 | Looks prime; digit-sum 12 gives it away |
| 119 | 7 × 17 | Passes the 2/3/5 quick checks |
| 1 | Neither | Definition requires two divisors |
| 2 | Prime | The only even prime |
Quick Divisibility Screens
Before any division: even numbers >2 are out; digit-sum divisible by 3 means divisible by 3; ending in 0 or 5 means divisible by 5. These three screens eliminate ~73% of all numbers instantly — the checker applies them first and shows which rule fired.
Why Primes Run the Modern World
RSA encryption secures web traffic on one asymmetry: multiplying two 300-digit primes is instant, factoring their product is computationally infeasible. Prime moduli also power hash functions and random number generators. Every checkout page you've used leaned on primality.
Free and Instant
Unlimited checks with full factor breakdowns, computed locally — for students, teachers, and the incurably curious.