Balanced prime checker
53 is a balanced prime: the nearest primes are 47 below and 59 above, both 6 away, and their average is 53. Enter a prime from 2 up to 1,000,000,000 to see its neighbours, their mean and the verdict. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Number
- 53
- Previous prime
- 47
- Next prime
- 59
- Neighbor average
- 53
A balanced prime sits exactly halfway between the prime immediately before it and the prime immediately after it. This checker validates that the supplied integer is genuinely prime, finds both neighboring primes, calculates their arithmetic mean, and compares that mean with the original value. It returns the evidence behind the decision rather than only a yes-or-no label. Composite numbers are rejected, which keeps the result faithful to the mathematical definition and makes input mistakes visible in automated workflows.
What makes a prime balanced
A prime number is balanced when its distance from the previous prime equals its distance from the next prime. The same condition can be written by saying that the middle prime equals the arithmetic mean of those two neighbors. For example, 53 has 47 immediately below it and 59 immediately above it.
Both gaps are six, and the average of 47 and 59 is 53, so the test succeeds. The word “immediately” matters: choosing any convenient lower and higher primes would not test the accepted definition. This checker therefore searches outward until it identifies the closest prime on each side, reports those values, computes their mean, and compares the mean with the submitted prime.
The returned fields make the conclusion easy to inspect or reuse. A false result does not mean the number is composite; it means the number is prime but is not centered between its neighboring primes. Composite input is handled separately as an error so these two mathematical facts are never confused.
How to enter and interpret a value
Provide one integer in the number field. Fractions, numeric strings, unsafe integers, values outside the range, and composite integers are rejected instead of being silently rounded or converted. Two is a valid prime yet has no preceding prime, so it cannot satisfy the two-neighbor definition.
In that special case the result is false, the next prime is reported, and fields for a nonexistent previous prime or average are omitted. This avoids inventing a sentinel value and keeps optional output semantically clean.
Deterministic checking for study and automation
The checker uses exact integer arithmetic and deterministic primality tests rather than random witnesses, external databases, or network lookups. It first verifies the supplied value, then tests neighboring candidates until it reaches the closest prime below and above. Divisibility only needs to be checked through the square root of each candidate, and even candidates are skipped after handling 2.
The tool is useful in lessons about prime gaps, sequence experiments, puzzle validation, and test-data pipelines where a transparent answer matters more than a bare classification. The upper bound is deliberate: it limits worst-case work while covering a broad range of ordinary examples. For research involving enormous integers or probabilistic primality methods, use specialized number-theory software designed for arbitrary precision instead.
What you can do with it
Check a number theory exercise
Verify a proposed balanced prime and see the exact neighboring primes that justify the answer.
Validate puzzle input
Reject composite submissions and distinguish valid but unbalanced primes from balanced ones.
Build a prime-sequence dataset
Classify individual primes with explicit neighbors and midpoint values for later analysis.
FAQ
What is a balanced prime?
It is a prime equal to the arithmetic mean of the immediately preceding and immediately following primes.
Why is 2 not balanced?
Two has no previous prime, so it cannot be the midpoint of a preceding and following prime.
Does the checker use a prime database?
No. It deterministically tests the input and neighboring candidates with local integer arithmetic.
What happens if I enter a composite number?
It is rejected with a clear message instead of a false result. A false answer is kept for primes that are not centred between their neighbours, so the two situations never get mixed up.
Why do the neighbours have to be the closest primes?
The definition uses the prime immediately before and immediately after. Picking any convenient lower and higher primes would not test it, so the checker searches outward until it finds the nearest one on each side.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/numth/balanced-prime \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"number":53}'const res = await fetch("https://api.kit.forhosting.com/numth/balanced-prime", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"number": 53
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/numth/balanced-prime",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"number": 53
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/numth/balanced-prime", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"number":53}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"number":53}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/numth/balanced-prime", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"number": 53
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "numth.balanced_prime",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Limits
max_value | 1000000000 |
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
How to enter and interpret a value
The accepted range begins at 2 and ends at 1,000,000,000, giving the deterministic algorithm a clear operating bound for browser and API use. For a prime greater than 2, the response includes previous_prime, next_prime, neighbor_average, and is_balanced alongside the original number. If is_balanced is true, the two prime gaps are equal; if it is false, the neighbors are still correct, but their midpoint differs from the submitted prime.
Deterministic checking for study and automation
Each request evaluates one item, and API use costs $0.002; the same core calculation can run locally in the page for interactive checks.
Technical questions
What happens if I enter a composite number?
The request returns an invalid_input error because balanced-prime status is defined here only for prime input.
How much does API use cost?
Each request costs $0.002. Interactive browser execution is also available without a network calculation.