Comprehensive Calculator Guide
This calculator tells you whether a number is prime or composite, gives its smallest factor if composite, and the previous and next primes. 97 is prime; 91 looks prime but is 7 × 13. It works up to a trillion.
Testing for primes
A prime has exactly two divisors, 1 and itself; 1 is neither prime nor composite. Testing primes up to the square root is enough. Euclid proved the primes never end, and modern encryption relies on them.
How to Use
- Enter a whole number.
- Nothing else is needed.
- Press “Check” to see its type, smallest factor and nearest primes.
Formula Used
Prime if no prime up to √n divides it
Practical Examples
- Example 1: 97
- Prime; 89 before, 101 after.
- Example 2: 91
- 7 × 13, composite.
- Example 3: 1
- Neither; the next prime is 2.
Important Tips
- Rule out even numbers and multiples of 5.
- Use the digit sum for 3.
- Test up to the square root.
Common Mistakes to Avoid
- Calling 1 prime.
- Assuming odd means prime.
- Forgetting 2 is prime.
Frequently Asked Questions
- Is 1 prime?
- No.
- Is 91 prime?
- No, 7 × 13.
- How many primes are below 100?
- 25.