Tips
To check a number for primality in your head, rule out small factors first: 2, 3, 5, then 7, 11 and 13 up to the square root. Most composites fail almost immediately.
Here's a fast, repeatable routine.
Step 1: knock out the easy ones
If it's even (other than 2), ends in 0 or 5, or its digits sum to a multiple of 3, it's not prime. That eliminates most candidates instantly.
Step 2: test up to the square root
Only check primes up to √n. For a number under 121, you only need 2, 3, 5 and 7. For under 289, add 11 and 13.
Step 3: use divisibility rules
Apply the 7 and 11 tricks from our divisibility rules guide to finish quickly.
Practice set
Are these prime? 91, 97, 143, 211. Answers: 91 = 7×13 (no), 97 (yes), 143 = 11×13 (no), 211 (yes). Verify with the Prime Number Checker.
Key takeaways
- Rule out 2, 3 and 5 first — most composites fail here.
- Only test primes up to the square root.
- Watch for sneaky products like 91 = 7×13 and 143 = 11×13.
- Confirm with a checker when unsure.
Frequently asked questions
How can I tell if a number is prime quickly?
Eliminate even numbers, multiples of 5 and multiples of 3 first, then test the remaining small primes up to the square root.
What primes do I need to test below 100?
Just 2, 3, 5 and 7 — because 11² = 121 is already above 100.
Why is 91 not prime?
Because 91 = 7 × 13, even though it looks prime at a glance.
The LCM Calculator Team
Math educators and engineers building free, accurate calculators with step-by-step solutions, visual diagrams and AI insights.
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