Twin Prime Finder
Find twin prime pairs (primes that differ by 2, like 11 & 13) starting from any number up to 1 billion. Get the first N pairs, the gaps between them, and Brun's-constant partial sum.
Input
Output
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/twin-prime-finder \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"start": "1",
"count": "10"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `twin-prime-finder` tool (Twin Prime Finder) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.
Embed widget
<iframe
src="https://iotools.cloud/embed/twin-prime-finder/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="Twin Prime Finder — iotools.cloud"
sandbox="allow-scripts allow-forms allow-same-origin allow-downloads allow-popups allow-popups-to-escape-sandbox"
allow="clipboard-write"
style="width:100%;border:1px solid #e5e7eb;border-radius:12px;overflow:hidden"></iframe>
<script src="https://iotools.cloud/embed.js" async></script>Drop this into your own page — free, no key required, just a link back.
| Cost per API/MCP call | From 5 credits |
|---|---|
| Need more credits? | View pricing |
Also available with
Guides
The Twin Prime Finder lists twin primes — pairs of primes that differ by exactly 2, such as (3, 5), (11, 13) and (17, 19). Pick a starting number and how many pairs you want, and the list appears instantly.
How to use it
- Enter Start from — the search begins at this number (up to 1,000,000,000).
- Enter Number of pairs (1–500).
- Read the pairs, the summary, and the details panel with the gaps between consecutive pairs and the partial sum of their reciprocals.
Commas and spaces in numbers are ignored.
What are twin primes?
A twin prime pair is two primes (p, p + 2). (3, 5) is the only pair that includes 3; every other pair has the form (6k − 1, 6k + 1). Whether there are infinitely many twin primes is the famous, still-open Twin Prime Conjecture.
What is Brun's constant?
Brun proved that the sum of reciprocals of all twin primes converges, to about 1.902. The details panel shows the partial sum for the pairs you listed, so you can watch it creep upward.
Why is the start limited to one billion?
Primality is checked by trial division in your browser; capping the start keeps every search instant. To test a single large number, use the Prime Checker, or list primes in a range with the Prime Factorization Calculator.
Privacy
Everything runs locally in your browser. Nothing you enter is uploaded.