Show HN: Goldbach Conjecture up to 4*10^18+7*10^13

5 days ago (medium.com)

Achieved a new world record in verifying the Goldbach Conjecture using grid computing, by extending the verification up to 4 quadrillion (4×10¹⁸) + 70 trillion (7×10¹³).

My grid computing system - Gridbach is a cloud-based distributed computing system accessible from any PC or smartphone. It requires no login or app installation. The high-performance WASM (WebAssembly) binary code is downloaded as browser content, enabling computation on the user’s browser.

[Website] https://gridbach.com/

[Medium] https://medium.com/@jay_gridbach/grid-computing-shatters-wor...

140 comments

jay_gridbach

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commonlisper  5 days ago

Cool project but... This is an egregious misrepresentation of the actual results both from significance perspective and accuracy perspective.

A. No validation is done on server side to confirm the workers are reporting correct results.

B. Increasing the limit by less than a thousandth of a percent does not make this a "world record"! If we go by that logic, I only have to validate one more example than you and claim a world record. And then you'd do the same. And then I'd do the same and we'll be playing "world record" ping pong all day!

But "B" isn't the big problem here because we have worse problems "A"! Nobody (not even the OP) can tell if the results are accurate!

No, I'm not simply dissing at a Show HN post. There are many comments here that explain these problems much better than I could.

This is egregrious clickbait!

  • lIl-IIIl  5 days ago

    "Increasing the limit by less than a thousandth of a percent does not make this a "world record"!"

    Why doesn't it?

    "If we go by that logic, I only have to validate one more example than you and claim a world record."

    Yes. You can argue that it's not difficult enough or interesting enough, but you can't argue that N+1 result is not a world record.

  • lanyard-textile  4 days ago

    If you’d read the article... ;)

    He slightly pushed the computation past the previous world record, and he’s continuing to push it forward with a clear goal. It’s well within the spirit of a world record.

    Besides, a world record is still a world record — it’s up to you to decide how interesting it is. You are indeed just dissing on a Show HN post.

    Server side validation is trivial. What makes you believe that is not happening? That code is not available.

    • throwaway150  4 days ago

      > If you’d read the article... ;)

      If you'd read the article carefully, he hasn't. For all we know one client (or worse, several) found counterexamples but didn't report them back to the server. Without verification on the server side, there's no way to claim the entire range has been reliably checked.

      What he's shown is that many volunteers have checked a large portion of the numbers up to a certain bound and found no counterexamples. But he hasn't shown that all numbers within that range have actually been verified. It's entirely possible that some block results were falsely reported by bad clients. Meaning counterexamples could still be hiding in those falsely reported gaps, however improbable! This kind of lapse in rigor matters in math! This lapse in rigor invalidates the entire claim of the OP!

      > Server side validation is trivial. What makes you believe that is not happening? That code is not available.

      Please read the full thread. This has all already been discussed at length.

      https://news.ycombinator.com/item?id=43736558

      Don't get me wrong. I've said before. This is a good project. But the claims made in the post don't hold up to scrutiny.

      > a world record is still a world record

      This isn't particularly relevant at the moment, since OP can't confirm the correctness of the results!

      1 reply →

kazinator  5 days ago

"No one has proven it mathematically up until now" is bad grammar in relation to the intended meaning. This idiom of English conveys the meaning "it has now been proven mathematically, but never before now; this is the first time".

What Hiroaki wants here is "no one has proven it mathematically". Full stop.

Or "no one has proven it mathematically to this day", or "no one has proven it mathematically so far".

  • jay_gridbach  5 days ago

    Thank you for your advice! It helped me to understand how native speakers take this sentense. I have just corrected to "no one has proven it mathematically to this day".

tromp  5 days ago

Does the gridbach server trust all submitted results to be correct, or can it somehow verify them (much faster than the outsourced computation) ? I managed to contribute 2B verifications in a few minutes.

  • oefrha  5 days ago

    I had a brief look at the network traffic and code. The network communication is very simple:

    To request a new batch:

      POST https://jqarehgzwnyelidzmhrn.supabase.co/rest/v1/rpc/get_job
  apikey: ...
  authorization: Bearer ...

  {"_client_hash":"..."}

    returns something like

      {
    "jobId": 755344,
    "message": "get_job() succeeded, got jobId: 755344 as a new one"
  }

    which means the client should check 4000075534400000000-4000075534500000000.

    Once done:

      POST https://jqarehgzwnyelidzmhrn.supabase.co/rest/v1/rpc/put_job
  apiKey: ...
  authorization: Bearer ...

  {"_client_hash": "...","_job_id": 755344,"_status": 1,"_elapsed_time": 19.54,"_p": 3463,"_q": "4000075534448687929"}

    Here, _client_hash is generated by wasmHash(`{"method":"Hash"}`) in /js/worker.js (yes, the payload is a fixed string), and while I didn't try to disassemble the wasm, one can pause execution and repeatedly call wasmHash() to observe it's basically a TOTP that changes every 10s, so it doesn't carry any mathematical information.

    Therefore, all the info that can be used for verification on the server is a single pair of _p and _q adding up to one number in the entire range. That's the extent of the verification.

    One can of course patch the code to check a single number before reporting that the entire range has been checked. Pretty sure it's impossible for the server to detect that.

    Correct me if I made a mistake somewhere.

    Edit: On second thought, maybe the specific number reported back is deterministically chosen in a way that relies on finishing all the checks in the range, and thus can be compared with other reported results for the same range?

    Even in that case, the server can't verify the work without repeating it. mersenne.org hands out a double checking job about 8 years later presumably to thwart determined attackers.[1]

    [1] https://www.mersenne.org/various/math.php

    • looofooo0  5 days ago

      Yeah, I mean what OP doing is statistically searching for counterexample at worst, but without verification about the completeness of the range. Only if we assign jobs randomly and multiple times, we may believe in the truth about the whole range, at least under the assumption, that there is enough people and no big enough attacker.

throwaway150  5 days ago

I truly hate to bring this up, knowing how much passion has gone into this project. But there's an important thread got buried due to arguments! That thread raises serious concerns about the validity of this bold claim.

As highlighted by @tromp and @oefrha (https://news.ycombinator.com/item?id=43734877) it is clear, clients can cheat. So we can't be 100% sure that none of the clients cheated. What if a counterexample to the conjecture exists, but a dishonest client simply failed to report it? Math results require rigor and without rigor no claim can be trusted. Without rigor, this bold assertion remains just that. A claim, not a fact.

OP! On top of that, you're being evasive in threads where you're being asked how your validation works and you went so far as to flag a pertinent thread. That definitely doesn't inspire confidence. Addressing the validation questions is absolutely 100% necessary if you want this to be seen as more than just a claim.

  • eddd-ddde  4 days ago

    Even if all clients are truthful and 100% correct, the lack of counter examples would still be essentially meaningless, right?

  • pavel_lishin  5 days ago

    It doesn't even have to be dishonesty; it could be a poorly timed cosmic ray flipping a bit.

    • GTP  4 days ago

      Yes, and I think this is actually more likely than someone intentionally modifying the code and finding a counterexample. Related, I'm now wondering what would happen if someone sent in a fake result claiming to have found a counterexample: will the website report the conjecture as proven false? It wouldn't last more than a few hours on the website, but I can totally see someone doing it as a prank.

      2 replies →

londons_explore  5 days ago

So this conjecture was validated up to 4,000,000,000,000,000,000.

And this project has increased that number to 4,000,010,000,000,000,000.

Increasing the limit by 0.00025%

Not totally sure this is a good use of the compute/brainpower...

  • JohnKemeny  5 days ago

    It's a better use of compute/brainpower than dissing someone's passion.

    • jay_gridbach  5 days ago

      @londons_explore @JohnKemeny Thanks you for your interst to my project! I have to admit the computation speed is slower than I expected. I have a plan to develop GPU version of computation client which could be much faster. Also I am happy to have feedbacks from for updating this project.

  • psalaun  5 days ago

    I thought the same. The resulting UX is really nice though, and the stack is interesting. If the author does publish other blog posts about the technical side, this project may help other people start their own distributed calculation project on more fruitful issues for the society, and I guess that'd be a win.

  • zamadatix  4 days ago

    Not that it changes much... but 7*10^13 instead of 10^13.

    I don't know about making a judgement call on what a good use of computer or brainpower is, it seems like a fun enough project in many ways, but in terms of claims worth headlining about the project I agree wholeheartedly.

krylon  5 days ago

When I learned programming, one of my first programs was a (rather lame) attempt to check the Goldbach conjecture. Over the years, as I learned more programming languages (first attempt was in C), it became my go-to program to get acquainted with a new language (for a few years, anyway). I never got very far, but it was fun to see how much performance I could squeeze out of the programming in various languages.

So this tickles my nostalgia bone strongly. And maybe makes me feel a tiny bit jealous. But more excited than envious, really, to see people are still working on this problem.

  • jay_gridbach  5 days ago

    Thank you for sharing your experience. It's quite moving to know that someone in another country was going through the same thing I was. I implemented Goldbach in C++, C#, Java, and Go.

    • krylon  5 days ago

      I did... let me think, it's been a while... C, Python, C++, Java, Common Lisp, Ada, Erlang. Also OCaml, Ruby, Haskell, Emacs Lisp, Lua, Rust, but I don't think any of those ever reached a working state.

      2 replies →

Karliss  5 days ago

I call BS on this one. Placing a penny on top of skyscraper doesn't make you a builder of highest building. Still an interesting (more than) weekend project but not a meaningful record.

Time required to compute next range grows very slowly and this project has only computed the incremental part from 4*10^18 to 4*10^18+7*10^13 . It would have taken previous record holder extra 0.002% time get those additional 7*10^13.

A meaningful record needs to either reproduce old one or beat it by significant margin. Otherwise you get meaningless +1 like this.

By my estimates (~7s to compute 10^8 large chunk) new "record" represents ~60days worth of single core compute. Run it on multiple threads and you essentially get 3-4days worth compute on single modern computer.

And it does so at rate which is much worse than previous record using 2012/2013 hardware. Previous record software was able to do 10^12 window in 48minutes on single i3 core from 2013. That's roughly 24x faster using the old software on 10year old low end computer compared to the new software on new hardware. Previous record represents ~133000 days of single core compute, probably less since majority of it likely run on something better than i3.

Unless author gets it to maliciously run on a popular website with at least 10^5 users(concurrently every minute not 10^5 unique during day), 5*10^18 doesn't seem reachable this way. Getting a data center to donate computing hours would also work, but in that case you could use more efficient native software like the one from 2013 (which was order of magnitude faster even then) or rewrite of it optimized for modern hardware. The current webassembly one only makes sense if you can get random individual volunteers do donate compute.

  • Turneyboy  5 days ago

    I absolutely agree. Not re-running the computation for the first 4*10^18 and claiming a new record is absolutely disingenuous. I could verify just a single example that hasn't been covered before and claim a new record with this logic.

    That is not to say that this is not a cool project. The distributed nature and running so seamlessly directly in the browser is definitely cool and allows people to contribute compute easily.

    It may be that grandiose claims of new records are needed to make people donate their computational resources but I am not a fan of deceptive claims like this.

    • jay_gridbach  5 days ago

      I know there haven't been any scientific progress yet, and I must admit that I gave it an easy-to-understand title to attract visitors to the site. I originally started this project out of curiosity to see what discoveries might lie ahead. For instance, my system is collecting `p` - least primes of a Goldbach partition. I am curious if there is any p larger than 9781. https://sweet.ua.pt/tos/goldbach.html

  • monster_truck  4 days ago

    To be equally pedantic, there is a historic practice of attaching spires to skyscrapers in order to claim this record within a city/country/etc

    • furyofantares  4 days ago

      Yes but the person placing the spire doesn't claim to have built the largest skyscraper unless they also built the rest of the skyscraper.

      Well, maybe they do on their resume.

      2 replies →

  • jay_gridbach  5 days ago

    Thank you for your comment. I will keep going to make this meaningful in some extent. The website message itself could be overstatement, but to be honest I am not trying to compete the predecessor. I am now trying to contact the predecessor to have feedback from him.

  • FabHK  5 days ago

    > Placing a penny on top of skyscraper

    Great intuitive metaphor, btw.

    • stuartjohnson12  5 days ago

      I wanted to see how this compares.

      ---

      Burj Khalifa - 828m

      US Penny - 1.52mm (0.00152m)

      Adding a US penny to the Burj Khalifa would therefore make it 0.000183% taller.

      --

      Original work - 4,000,000,000,000,000,000

      OP's work - 70,000,000,000

      OP's work added 0.00000175% to the current record.

      ---

      Conclusion: adding a penny to the Burj Khalifa is actually >100x more constructive than this effort.

      1 reply →

heikkilevanto  5 days ago

Running it now. On my phone (FairPhone 4) it took about 20 seconds for a round. On my desktop (Debian Liunux, KDE, Intel(R) Core(TM) i7-8700 CPU @ 3.20GHz), Firefox runs a round in about 12 seconds, and Chrome in 14.

I tried running in on 4 tabs on Firefox, and it did slow down a bit (maybe 16 seconds). All 4 tabs reported the same count, and it seemed not to increment for all the tabs. Also the initializing step was very fast on the subsequent tabs, as if it was reusing some data. Each tab used 100% of CPU and was doing different calculations. Same for Chrome.

Maybe it is not designed to be run in parallel on the same browser? Now I just run it on two separate browsers, one tab each. I probably stop later today when I need the computer for something else.

(Edit: Got a bit over 100B in 3.5 hours, stopping now. Machine running a tad warm, 25% CPU use, feels normal to use, but I think the fans are working a bit harder than normal)

  • jay_gridbach  5 days ago

    Thank yoy for trying! I am aware that it doesn't work correctly when opening the app in multiple tabs in same window.

jay_gridbach  5 days ago

I post this as a separate comment.

At this point, I am not capable with addressing the thing you pointed out - the way to block fake results in open network. From the very beginning, I don't want to make the system closed-network nor login required as I want people to join the calculation instantly. Technically, I think it is impossible to prevent reporting fake result as long as it is open network system - which means my design doesn't fit to seeking rigor.

If someone starts another project that handles calculations in better way, I would like to learn from it.

  • throwaway150  5 days ago

    Your project is not bad. It's the way you've worded this post and your article that comes across as misleading and deceptive.

    There's no definitive proof that a world record has been set. Nor that every individual block has been processed and reported honestly. What is known is that the system provides a mechanism for volunteers to submit counterexamples if they choose to. That's something.

    It's possible for clients to act dishonestly and withhold counterexamples. There's an incentive to claim independent credit. So the clients have incentive to lie.

    So your project doesn't ensure that every block has been verified, it allows honest participants to report findings. That's the reality and you should frame it that way in the post and article.

laurent_du  5 days ago

Impressive work! I did my share and added one billion verified numbers to your total, now you just need to get (almost) another billion of people to do the same and you'll achieve your next goal!

vlz  5 days ago

Running this now. I like how they have a big "Number of counterexamples found: 0" in the UI. Imagine they would find a counterexample on your machine… From time to time I switch to the tab to make sure the zero is still a zero (I guess there is basically no chance, but who knows?)

monster_truck  4 days ago

This is neat :)

X3D processors seem happy with running cores*1.5 tabs as long as you can keep it cool, was locked at 90C overnight and it never throttled below 4.2. Can see they're all doing different jobs, wish the display was better about updating the shared state!

I've submitted ~400,000,000,000 verifications so far, highest ridge is 5641 (18th on the dashboard). I think I've submitted far more than this and it isn't being counted correctly due to multiple tabs

E: The whinging about power consumption and killing the planet faster is so silly, a modestly sized OLED TV uses more power than this

yujzgzc  5 days ago

I thought there'd be a plot twist by the point I read 20 seconds into the article, letting me know that the algorithm was in fact already being run on my cell phone as I was reading about it... (Which would be a fine use of HN's traffic IMO!)

briansm  5 days ago

Interesting that the verified 4-quintillion range is well within 64-bit integer math range (18 quintillion or 9 quintillion signed), no need to go beyond regular 64-bit computing any time soon.

  • jay_gridbach  5 days ago

    Exactly. At this point WASM was the best choice for me to run the calculation with uint64 as I wasn't sure how much BigInt in JavaScript is efficient.

gnarlouse  5 days ago

Didn't seti@home get discontinued because the state of the art of computation progressed in the direction of cloud computing? Is the goal here to distribute the cost burden?

  • nroets  5 days ago

    You may be right e.g. SETI now requiring more RAM than it found in consumer computers.

    Also likely that seti@home was killed due to bandwith cost making it uneconomical[1]. After all they were looking for aliens in the data.

    This "gridbach" project is much closer to GIMPS.

    [1]: even if seti@home got their server bandwidth for free, they also need to factor in the bandwidth cost of their "home" participants.

schoen  5 days ago

How does the efficiency of the WASM version compare to running the same algorithm as native code?

  • jay_gridbach  5 days ago

    Comparing the performance of WASM Go version v.s. native Go command line version, the native code is faster. There should be certain overhead using WASM I guess.