Calculator Inputs
Formula Used
Primality test: A number is prime when it is greater than 1 and has no divisors except 1 and itself.
Nearest lower prime: Search downward from n - 1 until a prime is found.
Nearest higher prime: Search upward from n + 1 until a prime is found.
Nearest prime rule: Choose the prime with the smaller distance. If both distances match, both primes are returned.
Distance formulas:
- Distance to lower prime =
n - plower - Distance to higher prime =
phigher - n - Prime gap around the input =
phigher - plower
The script speeds up primality checking by rejecting even numbers and multiples of 3 early, then testing divisors with the 6k ± 1 pattern.
How to Use This Calculator
- Enter any whole number in the target field.
- Select whether you want the nearest, lower, higher, or both surrounding primes.
- Set the maximum search distance for larger inputs.
- Choose the graph window to control how many nearby integers appear.
- Set how many neighboring primes should be listed on each side.
- Tick the checkbox if a prime input should return itself.
- Press the calculate button to view the result above the form.
- Use the CSV or PDF buttons to export the calculated output.
Example Data Table
| Input | Lower Prime | Higher Prime | Nearest Prime(s) | Distance | Prime Gap |
|---|---|---|---|---|---|
| 12 | 11 | 13 | 11, 13 | 1 and 1 | 2 |
| 20 | 19 | 23 | 19 | 1 | 4 |
| 29 | 23 | 31 | 29 if self counted | 0 | 8 |
| 50 | 47 | 53 | 47, 53 | 3 and 3 | 6 |
| 100 | 97 | 101 | 101 | 1 | 4 |
Frequently Asked Questions
1. What is a nearest prime number?
It is the prime number closest to the chosen integer. The calculator checks the nearest prime below and above the input, then compares their distances.
2. What happens if the input is already prime?
If the self option is enabled, the calculator returns the input itself because its distance is zero. Otherwise, it shows the nearest prime neighbors around that prime.
3. Can two nearest primes exist at once?
Yes. When the lower and higher prime are equally far from the input, the calculator returns both values and marks the result as a tie.
4. Does the calculator work for negative integers?
Yes. Prime numbers start at 2, so negative inputs have no valid lower prime. The calculator searches upward and returns the nearest valid prime if found.
5. How is primality tested in this tool?
The script removes obvious non-primes first, then checks divisors only up to the square root. It uses the 6k ± 1 pattern to reduce unnecessary tests.
6. Why skip most even numbers during the search?
Every even number greater than 2 is composite. Skipping them makes the search faster, especially when the input is large and the prime gap is wider.
7. What does prime gap mean here?
Prime gap is the distance between the nearest lower prime and nearest higher prime around the input. It helps show how spread out nearby primes are.
8. What do the CSV and PDF options export?
They export the main result summary, including the input, surrounding primes, distances, tie status, and nearby prime lists for easier sharing or record keeping.