GIMPS on a supercomputer?

[Blackadder]

I recently joined my PC in the GIMPS. I was wondering though, since my computing power is slow and probably insignificant, won't all my PC's work become instantly redundant once GIMPS runs on a supercomputer? Or in the future, a quantum computer?

[VictordeHolland]

After your PC completes an assignment it will send the results to the GIMPS database.

So even if GIMPS (or a user) gets access to a supercomputer in the future (very unlikely) the assignments will not be duplicated, it will just accelerate the progress of the project.

BTW, GIMPS combined throughput of all users is about 400 TFLOPS, which is supercomputer territory (#500 in the TOP500 supercomputer list has ~548 TFLOPS)

[JM Montolio A]

Give me reasons to use a supercomputer for GIMPS. Many apps for a HPC are medical. Molecular Design. Chemicals. Physics simulation. Math modeling. Math equations. But for NT, few users. System benchmarking, is one.

[CRGreathouse]

Originally Posted by Blackadder

Or in the future, a quantum computer?

At the moment there is no threat from quantum computation, because only very large quantum computers would be useful for working on the size of numbers GIMPS is working on. It turns out that for all the many things they can do, quantum computers can't store numbers any larger than classical computers. In particular, if you program a one-million qubit quantum computer to remember 1000020-bit numbers, it can guess them with probability at most 1/1049576 -- the same probability a classical computer would have if it recorded the first million bits and guessed the last 20. (Not to be confused with superdense coding, in which 2n bits can be communicated with only n qubits by entangling them ahead of time with n qubits that the receiver has -- you see it takes 2n qubits in total to hold the information, just that only n of them need to be communicated.)

A 100 qubit quantum computer would be interesting (for quantum supremacy), a 1000 qubit quantum computer would be useful (for modeling quantum systems and quantum chemistry), and a one-million qubit quantum computer would be revolutionary, but it still wouldn't help GIMPS search for large primes AFAICT. (It would help factor small composite Mersenne numbers, which would be useful for enumerating pseudoprimes for example.)

[petrw1]

Originally Posted by VictordeHolland

After your PC completes an assignment it will send the results to the GIMPS database.

So even if GIMPS (or a user) gets access to a supercomputer in the future (very unlikely) the assignments will not be duplicated, it will just accelerate the progress of the project.

BTW, GIMPS combined throughput of all users is about 400 TFLOPS, which is supercomputer territory (#500 in the TOP500 supercomputer list has ~548 TFLOPS)

So couldn't we just use (borg) one of them? 😎

[Blackadder]

Some unexpected answers; cool. It feels good to contribute.

[lycorn]

Originally Posted by Blackadder

It feels good to contribute.

Yes, after all, that's what really matters. Don"t worry about the future, just enjoy the present Every computer counts!

[kladner]

Originally Posted by Blackadder

Some unexpected answers; cool. It feels good to contribute.

Welcome to GIMPS and to the forum! If you enjoy unexpected answers, you've come to a likely source. This diverse group produces diverse responses. These are some of the charms, (and irritations,) of the forum.

[henryzz]

Originally Posted by CRGreathouse

A 100 qubit quantum computer would be interesting (for quantum supremacy), a 1000 qubit quantum computer would be useful (for modeling quantum systems and quantum chemistry), and a one-million qubit quantum computer would be revolutionary, but it still wouldn't help GIMPS search for large primes AFAICT. (It would help factor small composite Mersenne numbers, which would be useful for enumerating pseudoprimes for example.)

On the subject of quantum computers, do we have any primality tests for quantum computers that will be able to prove primes we can't currently with 1M qubits?

[jasonp]

Originally Posted by henryzz

On the subject of quantum computers, do we have any primality tests for quantum computers that will be able to prove primes we can't currently with 1M qubits?

Use Shor's algorithm; if it cannot factor the input, then it is prime :)

Supercomputers are super because they are large and expensive; thus they are basically always reserved for computations that would be difficult anywhere else. If each node is a $15k server, and you have 10000 of them, along with switches that connect all of them to each other with a latency of microseconds and cost as much as the computers do, why would anyone in charge of such a machine devote time to tasks that 10000 volunteers would take on for free, with a latency of the internet?

[CRGreathouse]

Originally Posted by henryzz

On the subject of quantum computers, do we have any primality tests for quantum computers that will be able to prove primes we can't currently with 1M qubits?

Originally Posted by jasonp

Use Shor's algorithm; if it cannot factor the input, then it is prime :)

That works* up to 2^19 - 1, but beyond that you'll need more qubits. The best you can do is 2^p qubits for an exponent of p for Shor's algorithm modified with Kitaev recycling -- and frankly that setup seems extremely fragile, where a single error would probably destroy the whole answer. Maybe I should also cite Griffiths & Niu around the same time for the concept of qubit recycling. I'm not sure if it's entirely general but it certainly applies to the QFT in Shor's algorithm.

There's also the algorithm of Grosshans, Lawson, Morain, & Smith which is better by a constant factor than Shor's algorithm against semiprimes, and I think the recycling trick still works.

* Assuming your decoherence time is long enough for the calculation and your error rate is low enough. In practice you just run it a bunch of times like probable-prime tests.