Show HN: Goldbach Conjecture up to 4*10^18+7*10^13
132 comments
·April 19, 2025commonlisper
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
"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.
anyfoo
Yeah, I was confused, too. That’s how world records work.
throwaway150
That makes sense in sports. But in math? It's trivially easy to generate thousands of so-called "world records" every second.
Here's one:
4*10^18 + 7*10^13 + 1.
Boom! New world record. Now add 1 and you've got another. Try it. Keep going. World records like this will be surpassed by someone else in milliseconds.
Honestly, this is the first time I've heard "world record" used for NOT finding a counterexample. The whole thing feels absurd. You can keep checking numbers forever, calling each one a record? It's silly, to be honest. Never heard anyone calling these world records, before today.
OP has a nice project. But the wording is so deceptive and so silly that it harms the credibility of the project more than it helps.
peeters
I think they're saying that because it builds on the previous result having any one effort claim a record doesn't really make sense.
Like imagine there was a record for longest novel published, and what you did was take the previous longest novel and add the word "hello" to the end of it. Does the person who added "hello" get the record?
lanyard-textile
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
> 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=43735397
https://news.ycombinator.com/item?id=43735498
https://news.ycombinator.com/item?id=43735483
https://news.ycombinator.com/item?id=43735555
From the OP himself, an admission that there's no mechanism to ensure clients aren't submitting false results:
https://news.ycombinator.com/item?id=43736281
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!
lanyard-textile
Lol okay these comments do change things — I wish these were pointed out in the parent comment.
But I agree then. Good project; not a world record.
Edit: I’m not getting any of this for the article still, but I trust I’m misreading something
kazinator
"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
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".
ewalk153
If you want to imply some likelihood for it to be proven, you might write “yet to be proven”. Language subtleties…
kazinator
"to this day" creates an emphasis, like that it is surprising/amazing that such an old problem is not yet solved.
JohnKemeny
In this setting, the preferred word is "proved".
FeepingCreature
I would like to note, just for fun, that "proofed" also exists and means something else entirely.
pxeger1
"Proven" is not incorrect, although sometimes proscribed. https://en.m.wiktionary.org/wiki/proven#Usage_notes
weinzierl
Not a native speaker, here. Do you mean "proved" is preferred in a mathematical context?
ndsipa_pomu
The "to this day" is in my opinion unnecessary - you could phrase it as "no one has proved it mathematically".
Alternatively, "it has yet to be proved mathematically".
jay_gridbach
Thank you. Just removed "to this day".
tromp
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
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":"..."}
{
"jobId": 755344,
"message": "get_job() succeeded, got jobId: 755344 as a new one"
}
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"}
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]
looofooo0
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.
jay_gridbach
[flagged]
MauranKilom
But you posted this to a site that is literally called Hacker News... To be clear, I am not supporting any attempt at undermining your project, but people are pointing out to you that your results will be called into question if your only defence against "hacking" is "I hope people don't figure out how to do that".
tgv
That is understandable, but counterproductive. Tou can’t walk away from this by pretending it doesn’t exist. It only takes one troll to ruin the achievement.
oefrha
Note: The parent comment accused me of giving clues to hack the application, but that part was later edited out, making my response a bit strange.
---
This is basically a free security audit, even though I only spent like five minutes. If your application can be "hacked" so easily, it's very irresponsible to say you're "verifying" the conjecture. Removing the comment doesn't make your application any more secure.
Btw, I even helpfully pointed to prior art which you can learn from. A butthurt response is pretty sad.
gpvos
The most foolproof way to verify the results would be to have the client return all the 100 million values back to the server. This may be a bit much though, so alternatively, after submission, send a random selection of numbers in the range back to the client, which will have to return the prime summands* for those. Possibly with a time limit to prevent it from doing the calculation for only those numbers. So it probably also needs to be a fairly large selection.
*I had to look up that word
fragmede
Respectfully, you have put in an amazing amount of work. Unfortunately life is not so kind in other parts of the world, and people are just not nice on the Internet, and they will try and break your project just for the fun of it. It is very sad, but that is the reality of the Internet today.
jay_gridbach
Thanks for giving it a try. The Gridbach server only accepts computed result sent from my component.
Gehinnn
But how do you make sure the user actually runs your component without any modification?
jay_gridbach
All I can tell here is that I do certain level of valication on server side. As one of the goals of this project is to popularize the fun of mathematics among the general public, I think I would need to avoid a open network configuration to strictly conduct academic verification. The algorithm itself is publicly opened, so anyone can verify the computation step is correct or not. https://github.com/nakatahr/gridbach-core
montroser
That sounds interesting. How does that verification work?
throwaway150
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
Even if all clients are truthful and 100% correct, the lack of counter examples would still be essentially meaningless, right?
pavel_lishin
It doesn't even have to be dishonesty; it could be a poorly timed cosmic ray flipping a bit.
GTP
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.
akoboldfrying
Well, in the worst case, such a false positive can be discovered in at most the same amount of time as a typical block takes, by rerunning that same entire block in the server. And since we expect positives (false or otherwise) to occur very rarely, this should not be expensive.
Except... Doing this level of verification would enable DoSing the server very easily -- just send lots of false positives.
null
londons_explore
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
It's a better use of compute/brainpower than dissing someone's passion.
jay_gridbach
@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.
BoingBoomTschak
What if my passion is serial killing? Your brain is running on pure feelgoodium when you post such drivel.
psalaun
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.
jay_gridbach
Thank you for the kind comment! I'll put out a blog post about my tech stack sometime.
zamadatix
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
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
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
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.
jay_gridbach
I respect you have learnt a lot of programming languages throughout of your career.
Karliss
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
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
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
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
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.
monster_truck
I'm not sure this is in touch with reality, there are plenty of examples of companies who only poured the foundations of such buildings bragging about the entire thing.
jay_gridbach
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
> Placing a penny on top of skyscraper
Great intuitive metaphor, btw.
stuartjohnson12
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.
Philpax
Good lord, man, you don't have to be that much of an asshole about it.
heikkilevanto
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
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
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
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.
monster_truck
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
laurent_du
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!
jay_gridbach
Thanks for the cheer! I will keep going.
vlz
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?)
jay_gridbach
Haha, finding even a single counterexample would be a nightmare.
staunton
Surely, finding a counterexample would be huge news, a noteworthy advance in mathematics, and thus a great and widely praised achievement.
ndsipa_pomu
It'd also be an end to the project and would make the conjecture far less interesting.
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...