Hunting the largest prime number ever found, one exponent at a time.
The number the test is holding, printed in full decimal, every three quarters of a second. It has to look like noise until the very last squaring. If the last line reads 0, 2ᵖ−1 is prime.
Where on the number line, and what has been tested
Every Mersenne prime ever found is a tick on this line. The hatched band is where this machine is working now. The dashed line is where GIMPS hands out first-time tests today; the green one is the first prime worth US$150,000.
Money in, hours out
Every purchase funds a share of a GPU hour and is tested in the name of the address that paid. Every hour has a receipt: the NVDA sold, the transaction, the invoice.
What has been published
Every exponent tested, prime or not. The method, the factor or the 64-bit residue, the seconds it took, and whether GIMPS agrees. Composite is the normal answer; it is printed with the same care.
Positive control
Run the same test on Mersenne primes known for decades and get them back. Until then nothing this machine says counts.
Agreement with GIMPS
Every result compared with the public GIMPS record. One disagreement stops the program until it is understood.
Throughput
Squarings per second at the current size. It is what an hour buys, in numbers.
What this commits to, and how an hour is spent
Short on purpose. The long version is the code, which is public, and the record above, which is the only proof that matters.
Only prime exponents
2ᵖ−1 can only be prime if p is. Everything else is skipped before a cycle is spent.
Cheap first
Trial factoring before any long test. A factor found in seconds ends the question.
Residues printed
Every composite leaves a 64-bit residue. It is printed here so anyone can reproduce the run.
GIMPS decides
A prime is announced by GIMPS after independent verification. This page copies that, never precedes it.
Measured cost
Every GPU hour with its price, its receipt, and the NVDA sold to pay for it.
Rediscovery says so
Warm-up results are known answers. They are labelled as such, in the table and in the stamp.
The largest known prime has 41 million digits and was found in 2024 by one volunteer's GPUs, running the same open test everyone else runs. The next one is out there, in a range GIMPS has mapped but not finished. Nobody is paid to test it; the search is volunteers, electricity, and patience.
This project buys that electricity one GPU hour at a time and reports every result to PrimeNet, where it becomes part of the public record whether or not it is a prime. Almost every result will be composite. Those results still clear exponents nobody has to test again, and they are reported too.
Why NVIDIA stock. The fee has to be held in something. The test itself runs on NVIDIA cards: gpuowl and mfaktc are GPU programs, and every hour the fee buys is an hour on one of them. So the treasury sits in the stock of the company that makes the machine, tokenized, on-chain, countable, and only the slice the next hour costs ever leaves. Nothing about this is a partnership. NVIDIA has never heard of it.
Pick the exponent
From PrimeNet when connected; from the warm-up range until then. Only primes p.
Trial factoring
Any factor of 2ᵖ−1 has the form 2kp+1 and is ±1 mod 8. Test them up to a bit limit. A hit ends the test.
Lucas–Lehmer
s₀ = 4, then s ← s² − 2 (mod 2ᵖ−1), p−2 times. Zero at the end means prime. Nothing else does.
Keep the residue
The low 64 bits of the last s, in hex. It is the fingerprint GIMPS publishes for every composite.
Cross-check
Compare with the public record. Warm-up: the answer is known. PrimeNet: a second machine repeats the test.
Publish
Exponent, digits, result, method, residue or factor, seconds, cost. Here and on mersenne.org.
Buy the next hour
Sell only the NVDA it costs. Both transactions in the ledger before the GPU starts.
Each step priced, each step a receipt
Costs are what the project will spend. A step unlocks when its cost is covered; when it is paid, the receipt is printed with the date. measured is a real invoice, estimated is the provider's public rate, no compute costs only time, not ours cannot be bought, only earned.
The last rung is shown so the distance is honest. About one first-time test in sixty thousand is a prime; a 4090 finishes one test in about two days. If a prime ever comes out of an hour this page paid for, GIMPS will say so first, and this page will say so second, with the link.