Calculator Inputs
Example Data Table
| Number | Prime Status | Factors | Divisor Count | Notes |
|---|---|---|---|---|
| 2 | Prime | 1, 2 | 2 | Smallest prime number. |
| 29 | Prime | 1, 29 | 2 | No divisor up to √29 works. |
| 49 | Composite | 1, 7, 49 | 3 | 7 × 7 shows a repeated prime factor. |
| 60 | Composite | 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 | 12 | Many divisors make it strongly composite. |
Formula Used
A positive integer n is prime when it has exactly two positive divisors: 1 and n.
n is prime ⇔ there is no integer d with 2 ≤ d ≤ √n such that n mod d = 0
The calculator uses trial division. It checks divisibility from 2 through the square root of the input. If any divisor divides evenly, the number is composite. If none divides evenly, the number is prime.
How to Use This Calculator
- Enter the integer you want to test in the number field.
- Optionally set a start and end value to review nearby primes.
- Enable the step display if you want divisor testing details.
- Press Check Prime Number to show the result above the form.
- Use the CSV or PDF buttons to export the current report.
Frequently Asked Questions
1. What is a prime number?
A prime number is a positive integer greater than 1 with exactly two positive divisors: 1 and itself. Examples include 2, 3, 5, and 11.
2. Why does the calculator stop at the square root?
If a number has a divisor larger than its square root, the matching paired divisor must be smaller than the square root. That makes further checks unnecessary.
3. Is 1 a prime number?
No. The number 1 has only one positive divisor, not two. Because of that, it is neither prime nor composite.
4. Why is 2 special?
The number 2 is the smallest prime and the only even prime number. Every other even number is divisible by 2 and therefore composite.
5. Can this calculator test negative integers?
Yes, it accepts them, but negative values are not classified as prime. Standard prime definitions apply only to positive integers greater than 1.
6. What does the prime position mean?
If the tested value is prime, the calculator shows its order in the prime sequence. For example, 11 is the 5th prime number.
7. What is shown in the range snapshot?
The range snapshot lists all prime numbers between the chosen start and end values. It also reports how many primes appear in that interval.
8. When should I export the result?
Export when you want a saved copy for homework, documentation, classroom examples, or quick reference during number theory work.