καταστερισμός — a placing among the stars
The sieve that finds
them is his too.
Eratosthenes catalogued the constellations and invented the method for finding prime numbers. Twenty-two centuries later, a small C program runs his sieve on machines that would otherwise be idle, looking for constellations made of primes — and pays for the search in the coin it mines.
LIVE TESTNET · EXPERIMENTAL · TEST COINS HAVE NO MONETARY VALUE
Six primes in fixed formation. The gaps never vary: 4, 2, 4, 2, 4. The current testnet accepts the first four as a share and the first five as a block. All six form the full sextuplet pattern. The smallest is 7, 11, 13, 17, 19, 23 — and it is the only one that does not obey the rule on the next plate.
Cyrene, c. 276 BCE — Alexandria, c. 194 BCE
A librarian who measured
the world with a shadow.
Eratosthenes ran the Library of Alexandria. His rivals nicknamed him Beta — second-best at everything, never first at one thing. The joke has not aged well. Three of the things he was second-best at are, between them, this entire project.
The Sieve
κόσκινον Ἐρατοσθένους
Write the numbers out. Strike every multiple of two, then of three, then of five. Continue through the primes up to the square root of your limit. The unstruck numbers greater than one are prime — a simple idea that still underlies modern sieves.
Here: a wheel built from 2·3·5·7 eliminates 77% of candidates before a single primality test runs.
The Catasterismi
Καταστερισμοί
A catalogue of the constellations and the myths that put them there — a catasterism is the act of placing a figure permanently into the sky. The surviving work is traditionally attributed to Eratosthenes.
Here: the project's name, and its unit of work. Every accepted find is fixed in the chain the way a figure is fixed in the sky.
The Measurement
περὶ τῆς ἀναμετρήσεως τῆς γῆς
At noon on the solstice the sun stood directly over a well at Syene. At Alexandria, it did not — it cast a shadow of about 7.2°. From that angle and one road distance he computed the circumference of the Earth.
Here: the method. Small idle observations, carefully combined, answer a question far larger than any one of them.
Run his sieve.
Below are the numbers 1 to 210. Strike the multiples of 2, 3, 5 and 7 and what survives shows the first stages of his sieve. Then remove the four small primes themselves and include 1: the remaining 48 residues form a wheel for skipping multiples. A wheel survivor can still be composite. Every prime sextuplet above 7 starts at one specific residue in this wheel.
What the node is
actually looking for.
A prime constellation is a set of primes in fixed relative positions. This one has six members and a span of sixteen. They are rare, they get rarer as the numbers grow, and there is no way to find one except to look.
The wheel does the eliminating
210 is 2·3·5·7. Only 48 of the 210 residues are coprime to it, and a sextuplet must land on exactly one of them: 97. Everything else is struck before any arithmetic happens.
Then it is just testing
Candidates pass through a larger sieve and then a base-2 Fermat probable-prime test. Most fail before forming a constellation. Throughput depends on the processor, current difficulty and available thermal headroom.
Work is proof, not promise
A share carries a candidate quadruplet. Each node checks it against the protocol's probable-prime tests, work and linkage rules. These tests are not a mathematical certificate of primality.
It runs on the machine you have
A small static binary with mining workers at idle scheduling priority. Memory and disk use grow with chain history; validation-only nodes can run without mining.
Idle means idle
A small program.
A growing chain.
The executable is small; running a network still takes resources. These are current testnet measurements and controls, not fixed limits on future storage, memory or electricity use.
Statically linked against musl and stripped. ldd reports “not a dynamic executable” — there is no libc to install, no runtime, no interpreter. It is one file, and a build gate fails if it grows past 192 KiB. These are the tested x86 and ARM builds.
Observed container memory on the Nixos testnet miner with two workers, on 2 October 2026. Chain history, peers and replay affect usage. Budget disk and RAM separately for the Explorer and its database.
Mining workers request Linux's idle scheduling class and lowest nice priority. Duty settings and container CPU limits bound their work; mining still consumes electricity and produces heat.
The default thermal target is 82 °C, with configurable limits. The controller reduces mining duty as the chip warms and pauses if its sensor becomes unavailable. Hosts without a trustworthy sensor can validate and relay with mining disabled.
Thirty for the chain, seventy for the question
Two searches.
One reward budget.
Each testnet block allocates 30% of its reward to chain security and 70% to a separate prime-gap search. The same node can contribute to both lanes.
The consensus lane
Pays the miners who secure the chain, shared out by the work each one actually did over the last 256 shares.
The science lane
Funds a search for prime gaps — long stretches of consecutive composite numbers, the emptiest reaches between primes. A claim names a gap that nodes check under the protocol's probable-prime and composite-testing rules, with a bounded verification cost. This is not a certified prime-gap record.
Within the fixed search region size, payout weight increases exponentially with gap length. Accepted claims in the payout window share the released reward.
Each block adds 35 test coins to the science escrow. When eligible claims exist, a tenth of its balance is released. With claims at every block, the retained balance approaches 315 and the payout approaches 35 per block. Without eligible claims, funds accumulate until a later payout.
Run a node.
The project is in an extended testnet campaign. Start with the source and setup instructions; mining needs a real temperature sensor, while a validation-only node can follow the chain without one. Test coins have no monetary value.
Source and node setup on GitHub ↗
You can inspect the live chain before installing anything. The Explorer serves HTML to a browser and a text dashboard to a terminal:
# inspect the live testnet
curl -fsS https://explorer.catasterism.xyz/
The explorer is a separate Go implementation that follows a node and re-derives the entire chain from scratch — the work, the linkage, the commitments, the balances. It never trusts the node's arithmetic. If the two ever disagree, the dashboard says so on its first line.
- Constellation
- p, p+4, p+6, p+10, p+12, p+16
- Share / block
- quadruplet / quintuplet (testnet)
- Share spacing
- 4 s target
- Payout
- PPLNS over 256 shares
- Reward split
- 30% chain · 70% science
- Node binary
- 162–178 KiB, static, musl
- Resident memory
- grows with chain history
- Network
- testnet · a8f4562e57e74f9d