Prime Numbers Checker Form
Example Data Table
| Input Case | Checked Number | Range | Expected Result |
|---|---|---|---|
| Single prime check | 29 | 1 to 50 | 29 is prime. Range contains 15 primes. |
| Composite detection | 30 | 20 to 40 | 30 is not prime because 2 divides exactly. |
| Edge value | 1 | 1 to 10 | 1 is not prime. Range still lists 2, 3, 5, 7. |
| Local prime gap study | 100 | 90 to 120 | Nearest primes are 97 and 101. |
Formula Used
A number n is prime when n > 1 and no integer divisor exists in the interval 2 ≤ d ≤ floor(√n).
Prime test rule: n is prime if n mod d ≠ 0 for every tested divisor d up to floor(√n).
Range count: Prime count equals the number of integers in the selected interval that satisfy the prime test rule.
Prime density: density = (primes in range ÷ total integers in range) × 100.
How to Use This Calculator
- Enter a whole number to test whether it is prime.
- Add a range to scan nearby values and visualize prime distribution.
- Choose a preview limit for divisor rows and listed primes.
- Submit the form to display results above the form.
- Use the CSV and PDF buttons to save the generated report.
Frequently Asked Questions
1. What makes a number prime?
A prime number is greater than 1 and has exactly two positive divisors: 1 and itself. If another whole divisor exists, the number is composite.
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 is smaller than the square root. Testing beyond that point is unnecessary.
3. Is 1 a prime number?
No. Prime numbers must have exactly two positive divisors. The number 1 has only one positive divisor, so it is not prime.
4. Are negative numbers prime?
No. Standard prime-number definitions apply only to positive integers greater than 1. Negative values can still be factorized, but they are not prime.
5. Why is 2 special?
The number 2 is the only even prime. Every other even number is divisible by 2 and is therefore composite.
6. What does the prime density value mean?
Prime density shows how many values in the selected range are prime compared with the total number of integers analyzed. It helps compare different intervals quickly.
7. What do the CSV and PDF downloads contain?
The downloads include the summary metrics and available previews, such as listed primes and divisor checks. They are useful for homework, reports, or documentation.
8. Can I use the calculator for large ranges?
Yes, but the range is limited for browser responsiveness. Keeping the span moderate produces faster charts, smaller reports, and smoother page performance.