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.
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.
That's not comparable to finding Goldbach NON-counterexamples.
With Goldbach, claiming a "world record" just means checking one more number and seeing if it is still NOT a counterexample. It's easy. Contrast that with computing a new digit of pi - something you can't achieve by simply incrementing a value and running a check.
Finding each new digit of pi (the ones very far out) is not a trivial task. The computational effort increases by a lot as you go deeper. Something like O(n (log n)^k) for some k (usually k = 3).
Since this is math, I feel pedantic. It may not be a notable world record, but it’s still a world record. There are infinitely many non-notable world record categories. I currently hold the one for saying the word “fbejsixbenebxhsh” the most number of times in a row. Nobody cares, but it’s still a world record.
Since it's not just math but also using English on a social website, we can be even more pedantic and observe that posting it implies notability. It is literally noting it.
This is more like if someone pulled a truck down 2,800 miles of road between NYC and LA in 2012, left it there, and then you grabbed the rope in 2025 to pull it less than another tenth of a mile to have "shatters world record" in your blog title.
I.e. not only is this an extremely small increment but the original work did not have to be repeated. Nothing about the state of computing in 2012 would have prevented going the extra amount here, they just decided to stop. The original record even states (on https://sweet.ua.pt/tos/goldbach.html):
> On a single core of a 3.3GHz core i3 processor, testing an interval of 10^12 integers near 10^18 takes close to 48 minutes
So the additional work here in 2025 was the equivalent of running a single core of a 2012 i3 for ~70 more hours.
All this is a shame as the project itself actually seems much more interesting than leading claims.
> That is the literal definition of a world record here, my guy.
I don't dispute that. If you read my comment carefully, you'll find that I'm calling them "world records" too. My point is that nobody in the math community uses "world record" for finding trivial non-counterexamples like this. There are infinitely many such "world records" and each one is trivial to surpass in under a second.
Compare that to something like the finding a new Mersenne prime or calculating more digits of pi. Those records hold weight because they're difficult to achieve and stand for years.
This post could've been one of the infinite, uninteresting "world records" if the OP had applied more rigor in the implementation. But due to gaps in verification, this post is not a world record of any kind because the correctness of the results can't be confirmed. The OP has no way to confirm the correctness of their data. You'd get better context by reading the full thread. This has already been discussed at length.
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?
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.
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.
"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".
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".
Btw despite the helpful pedanticism[1] of HN, I think your English is impeccable and idiomatically natural for someone who has probably not spent much time in immersive spoken English environments.
To people who accept "proven" as the past participle of "prove", there is no difference. The only reason it would be rejected in English writing about mathematics might be that a good many of mathematicians are also pedants for prescriptive grammar. It is not a mathematical issue whatsoever.
Not who you were replying to, but yes, it's a special case. For anything not having to do with a formal math-like proof, you want "has proven" instead of "has proved." It's super weird.
We only have a few of these in English, where one of the tenses of the verb changes depending on the subject matter, but they do exist. The only other one I can think of off the top of my head is hang: past and participle "hanged"/"have hanged" (to execute or be executed via hanging from the neck) versus "hung"/"have hung" (any other meaning).
Hope that helps!
Edit: fixed my example to better match the original text.
This doesn't match my experience, and no dictionary I've checked says the past participle depends on the context; only that "proven" and "proved" can both be used (in any context). See e.g. https://en.wiktionary.org/wiki/proven#Verb
I'm not a mathematician though, so maybe this is a genuine semantic convention that neither I nor my dictionary are aware of. Maybe it's just that some mathematical style guides say to prefer "proved", for consistency, not that it really depends on the context?
It seems to me that in North American English, we use the proven participle as an adjective (almost exclusively?). So that is to say a remedy, having been proved effective, is then considered "proven effective". This usage is drilled into people's heads by advertisements.
It feels sort of like the difference between gilded and golden. Something that has been gilded now has a golden surface. Now golden has that en suffix like some participles, but isn't one. It's a pure adjective.
But, "I have given", "I have woven", "I have forgiven", and indeed "I have disproven" (also disproved). "-n" for a past participle of a verb like this is neither universal nor unique to prove. I believe you just have to learn English's irregular verbs; there are no useful rules to follow.
There's a pattern that the verbs with the en participles do not have ed regular past tenses. They have ove, ote, ode, it, id past tenses.
There are exceptions though like swell, swelled, swollen. It's fuzzy enough that any -en past participle will sound fine if you just get used to hearing it.
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.
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]
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.
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
Never trust the client. You must do a full verification. IIUC from another comment, you only ask the client to return the interval they tested and some token to ensure the server send them that interval.
The idea is that it's very hard to find the two primes and it's very hard to prove that they are actually primes. But if the client send you both primes and send you each primality certificate, then the verification is very fast. Also, you can store that info so people can see it.
It would still take a nontrivial amount of computation to do all the verification afterwards. Back of the envelope calculations suggest it should less than 100x longer to find the two primes than to verify them.
It'd be neat to do the verification in the same manner by redistributing one client's results to another, therefore obtaining a proof modulo client collusion.
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.
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.
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.
Yes, checking a specific false positive would be trivial and extremely fast[0], as it's just about summing two numbers. But, if the server doesn't do the check, having the site report a counterexample to Goldbach's conjecture would be an easy prank to pull off.
[0] Verifying that those two numbers are actually primes may take more time, but it seems to me that we're still dealing with number sizes for which primality testing isn't that hard. After all, the code here seems to just be using Erathostene's sieve to find primes.
@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.
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.
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.
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.
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.
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.
My knowledge of most of these is superficial or seriously outdated. Particularly OCaml, Haskell, and Rust (AND C++!!!) are not languages I would claim to really "know". When I was younger, I tried to get to know as many languages as possible, at least in passing, but I have not used many of these in a professional context.
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.
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.
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
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.
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.
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)
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.
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.
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!
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?)
Possibly, but it would join other false conjectures such as Euler's sum of powers conjecture - posed in 1769 and no counterexample found until 1966. There's only been three primitive counterexamples found so far.
Not even the same implications. All empirical evidence strongly support the Goldbach conjecture. Any counterexample would mean an entire field of Mathematics has to be rewritten.
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
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!)
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.
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?
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.
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!
"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.
Yeah, I was confused, too. That’s how world records work.
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.
> Never heard anyone calling these world records, before today.
You've never heard of the world record for calculating digits of pi?
https://www.livescience.com/physics-mathematics/mathematics/...
That's not comparable to finding Goldbach NON-counterexamples.
With Goldbach, claiming a "world record" just means checking one more number and seeing if it is still NOT a counterexample. It's easy. Contrast that with computing a new digit of pi - something you can't achieve by simply incrementing a value and running a check.
Finding each new digit of pi (the ones very far out) is not a trivial task. The computational effort increases by a lot as you go deeper. Something like O(n (log n)^k) for some k (usually k = 3).
Every second is easy. Let's aim for new world records at a 1MHz rate.
Since this is math, I feel pedantic. It may not be a notable world record, but it’s still a world record. There are infinitely many non-notable world record categories. I currently hold the one for saying the word “fbejsixbenebxhsh” the most number of times in a row. Nobody cares, but it’s still a world record.
Since it's not just math but also using English on a social website, we can be even more pedantic and observe that posting it implies notability. It is literally noting it.
Isn't it more a record about the state of computing than the state of conjecture?
This is more like if someone pulled a truck down 2,800 miles of road between NYC and LA in 2012, left it there, and then you grabbed the rope in 2025 to pull it less than another tenth of a mile to have "shatters world record" in your blog title.
I.e. not only is this an extremely small increment but the original work did not have to be repeated. Nothing about the state of computing in 2012 would have prevented going the extra amount here, they just decided to stop. The original record even states (on https://sweet.ua.pt/tos/goldbach.html):
> On a single core of a 3.3GHz core i3 processor, testing an interval of 10^12 integers near 10^18 takes close to 48 minutes
So the additional work here in 2025 was the equivalent of running a single core of a 2012 i3 for ~70 more hours.
All this is a shame as the project itself actually seems much more interesting than leading claims.
It’s not a notable world record, but it’s still a world record, if we’re being pedantic. And math is pedantic.
That is the literal definition of a world record here, my guy.
Take it up with the rules.
And yes, mathematically it's uninteresting. But that's not what is being showed off here.
> That is the literal definition of a world record here, my guy.
I don't dispute that. If you read my comment carefully, you'll find that I'm calling them "world records" too. My point is that nobody in the math community uses "world record" for finding trivial non-counterexamples like this. There are infinitely many such "world records" and each one is trivial to surpass in under a second.
Compare that to something like the finding a new Mersenne prime or calculating more digits of pi. Those records hold weight because they're difficult to achieve and stand for years.
This post could've been one of the infinite, uninteresting "world records" if the OP had applied more rigor in the implementation. But due to gaps in verification, this post is not a world record of any kind because the correctness of the results can't be confirmed. The OP has no way to confirm the correctness of their data. You'd get better context by reading the full thread. This has already been discussed at length.
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?
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.
> 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!
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
"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".
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".
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".
Thank you. Just removed "to this day".
Btw despite the helpful pedanticism[1] of HN, I think your English is impeccable and idiomatically natural for someone who has probably not spent much time in immersive spoken English environments.
1. pedantry
Yes absolutely. I did not intend my suggestion to be interpreted as any kind of criticism.
If you want to imply some likelihood for it to be proven, you might write “yet to be proven”. Language subtleties…
"to this day" creates an emphasis, like that it is surprising/amazing that such an old problem is not yet solved.
In this setting, the preferred word is "proved".
"Proven" is not incorrect, although sometimes proscribed. https://en.m.wiktionary.org/wiki/proven#Usage_notes
"Proved" means demonstrated with a formal mathematical argument.
"Proven" refers to something confirmed over time, often used more informally.
"Proofed" is an editorial term—preparing text for publication.
To people who accept "proven" as the past participle of "prove", there is no difference. The only reason it would be rejected in English writing about mathematics might be that a good many of mathematicians are also pedants for prescriptive grammar. It is not a mathematical issue whatsoever.
I would like to note, just for fun, that "proofed" also exists and means something else entirely.
Not a native speaker, here. Do you mean "proved" is preferred in a mathematical context?
Not who you were replying to, but yes, it's a special case. For anything not having to do with a formal math-like proof, you want "has proven" instead of "has proved." It's super weird.
We only have a few of these in English, where one of the tenses of the verb changes depending on the subject matter, but they do exist. The only other one I can think of off the top of my head is hang: past and participle "hanged"/"have hanged" (to execute or be executed via hanging from the neck) versus "hung"/"have hung" (any other meaning).
Hope that helps!
Edit: fixed my example to better match the original text.
This doesn't match my experience, and no dictionary I've checked says the past participle depends on the context; only that "proven" and "proved" can both be used (in any context). See e.g. https://en.wiktionary.org/wiki/proven#Verb
I'm not a mathematician though, so maybe this is a genuine semantic convention that neither I nor my dictionary are aware of. Maybe it's just that some mathematical style guides say to prefer "proved", for consistency, not that it really depends on the context?
Also not aware of it, but am mathematically trained and would always say "proved".
It seems to me that in North American English, we use the proven participle as an adjective (almost exclusively?). So that is to say a remedy, having been proved effective, is then considered "proven effective". This usage is drilled into people's heads by advertisements.
It feels sort of like the difference between gilded and golden. Something that has been gilded now has a golden surface. Now golden has that en suffix like some participles, but isn't one. It's a pure adjective.
I would also always use that in a mathematical context but feel it’s weird to hear, say, “proved in a court of law”.
Grammatically, or semantically?
The curious situation is that verbs similar to prove have past participles which are just the same as the past tense. Even approve!
You don't say "your application has been approven".
Or "the problem has been solven".
Or "the quantity halved again, like it had halven before".
Or "that function has misbehaven again".
Or "I have moven the funds to the correct account".
Yet, "proven" is accepted.
But, "I have given", "I have woven", "I have forgiven", and indeed "I have disproven" (also disproved). "-n" for a past participle of a verb like this is neither universal nor unique to prove. I believe you just have to learn English's irregular verbs; there are no useful rules to follow.
Give has an irregular past tense though. I think if the past tense were gived, probably the past participle would be the same.
Same with: write, wrote, written; smite, smote, smitten; bit, bit, bitten; hide, hid, hidden; ride, ride, ridden; drive, drove, driven.
There's a pattern that the verbs with the en participles do not have ed regular past tenses. They have ove, ote, ode, it, id past tenses.
There are exceptions though like swell, swelled, swollen. It's fuzzy enough that any -en past participle will sound fine if you just get used to hearing it.
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.
I had a brief look at the network traffic and code. The network communication is very simple:
To request a new batch:
returns something like which means the client should check 4000075534400000000-4000075534500000000.Once done:
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
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.
Thanks for giving it a try. The Gridbach server only accepts computed result sent from my component.
But how do you make sure the user actually runs your component without any modification?
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
Never trust the client. You must do a full verification. IIUC from another comment, you only ask the client to return the interval they tested and some token to ensure the server send them that interval.
You must ask for each number in the interval the two primes and a Primality certificate for each prime. https://en.wikipedia.org/wiki/Primality_certificate
The idea is that it's very hard to find the two primes and it's very hard to prove that they are actually primes. But if the client send you both primes and send you each primality certificate, then the verification is very fast. Also, you can store that info so people can see it.
Thanks. Your advice is really helpful.
zk-SNARKS maybe?
For demonstrating verification of a conjecture, surely you can do much simpler things than a zero-knowledge proof: Send one of the primes.
It would still take a nontrivial amount of computation to do all the verification afterwards. Back of the envelope calculations suggest it should less than 100x longer to find the two primes than to verify them.
It'd be neat to do the verification in the same manner by redistributing one client's results to another, therefore obtaining a proof modulo client collusion.
Say smaller prime is less then 10,000. Then this one or two Byte per Nummer. E.g. 100 Mio number is already 100mb or
I am curious about alternatives or solutions in such a setting / context.
That sounds interesting. How does that verification work?
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.
Even if all clients are truthful and 100% correct, the lack of counter examples would still be essentially meaningless, right?
It doesn't even have to be dishonesty; it could be a poorly timed cosmic ray flipping a bit.
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.
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.
Yes, checking a specific false positive would be trivial and extremely fast[0], as it's just about summing two numbers. But, if the server doesn't do the check, having the site report a counterexample to Goldbach's conjecture would be an easy prank to pull off.
[0] Verifying that those two numbers are actually primes may take more time, but it seems to me that we're still dealing with number sizes for which primality testing isn't that hard. After all, the code here seems to just be using Erathostene's sieve to find primes.
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...
It's a better use of compute/brainpower than dissing someone's passion.
@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.
What if my passion is serial killing? Your brain is running on pure feelgoodium when you post such drivel.
That was mean.
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.
Thank you for the kind comment! I'll put out a blog post about my tech stack sometime.
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.
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.
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.
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.
I respect you have learnt a lot of programming languages throughout of your career.
My knowledge of most of these is superficial or seriously outdated. Particularly OCaml, Haskell, and Rust (AND C++!!!) are not languages I would claim to really "know". When I was younger, I tried to get to know as many languages as possible, at least in passing, but I have not used many of these in a professional context.
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.
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.
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
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
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.
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.
That's kinda like I said, maybe on their resume.
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.
> Placing a penny on top of skyscraper
Great intuitive metaphor, btw.
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.
Good lord, man, you don't have to be that much of an asshole about it.
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)
Thank yoy for trying! I am aware that it doesn't work correctly when opening the app in multiple tabs in same window.
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.
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.
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!
Thanks for the cheer! I will keep going.
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?)
Haha, finding even a single counterexample would be a nightmare.
Surely, finding a counterexample would be huge news, a noteworthy advance in mathematics, and thus a great and widely praised achievement.
It'd also be an end to the project and would make the conjecture far less interesting.
IMO it would make the conjecture far more interesting, as it would be a surprise to most people who have thought about the problem.
Many natural questions would arise, starting with “Is this the only counterexample?”
Possibly, but it would join other false conjectures such as Euler's sum of powers conjecture - posed in 1769 and no counterexample found until 1966. There's only been three primitive counterexamples found so far.
(I got that from https://math.stackexchange.com/questions/514/conjectures-tha... which features some other false conjectures that may be of interest to you)
Not even the same implications. All empirical evidence strongly support the Goldbach conjecture. Any counterexample would mean an entire field of Mathematics has to be rewritten.
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
Cool project. In your tooltip for "My Top 30 largest Goldbach ridges" you have `yilded` instead of `yielded`.
Thanks. I fixed it :-)
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!)
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.
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.
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?
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.
How does the efficiency of the WASM version compare to running the same algorithm as native code?
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.
Honest question— how is this verified for accuracy ? What if there is a bug ?
Thank you for your interst. I disclosed the core verification algorithm to make the procedure reviewable. https://github.com/nakatahr/gridbach-core
> 4 quadrillion (4×10¹⁸) + 70 trillion (7×10¹³)
That's 4 quintillion.
Thank you, I have just fixed it.
You also need to fix this sentence:
"i aim to push this farther to 5 quadrillion."
Thank you, I have just fixed it. This is so helpful, thank you from the bottom of my heart.
Keep doing stuff you like.
I contributed 32B. My work here is done
Thanks for sharing your computation resource!
Run a Tor node and mine BTC, too. :D
Grok says:
Final Answer: 4.00007×10^18
:-D
What's the point of that exercise? Just so we boil faster?
So cool!