One year, 41M digits: How Luke Durant found the largest known prime number

Recent and related:

GIMPS Discovers Largest Known Prime Number: 2^136279841 – 1 - https://news.ycombinator.com/item?id=41904237 - Oct 2024 (11 comments)

New Mersenne Prime discovered (probably) - https://news.ycombinator.com/item?id=41858024 - Oct 2024 (120 comments)

We changed the url above from https://www.popsci.com/science/largest-prime-number/ to the article it points to.

> Durant, who made his money off the boom, said he put his time and money into the project to show people that they aren’t helpless to technology giants and that we can figure out massive problems if we work together.

I can appreciate the sentiment but

> The discovery was the result of almost exactly one year of work and about $2 million of Durant’s own money.

doesn't really show me much especially since

> The prime number Durant discovered serves no real purpose for society.

This sort of shows the opposite: if it takes $2M to discover something that doesn't have a real purpose, yeah I definitely feel a bit helpless against tech giants trying to do anything that is marginally useful.

> The discovery was the result of almost exactly one year of work and about $2 million of Durant’s own money.

> Durant, who made his money off the boom, said he put his time and money into the project to show people that they aren’t helpless to technology giants and that we can figure out massive problems if we work together.

If I sold absolutely everything I owned, I would not even have close to half of what it Durant invested in his pet project. While I like his intended sentiment, I can't help but notice the irony.

Ha, we both basically posted the same thing ( see above )!

> The discovery was the result of almost exactly one year of work and about $2 million of Durant’s own money. ... The prime number Durant discovered serves no real purpose for society.

Not sure how to react to this.

He was also interviewed by Numberphile when it was first published. The interview was released in both a full and a cut version.

https://youtube.com/playlist?list=PLt5AfwLFPxWIWS5Jd3k5QHdc0...

"If I sold absolutely everything I owned"

Quite. I get the point but why not volunteer (to do something) and really show your grit?

Pissing around with M primes and trying to make a point is a bit wank as a stance from a multi-zillionaire.

He isn't helpless (to technology giants and that we can figure out massive problems if we work together.)

... and that's lovely.

I understand some negative comments here, that this was somewhat pointless waste of money. But I would argue that him spending 2M$ is in the same category of people spending money to do climb a mountain nobody did climb, or beat world circumnavigation record etc. I.e. this is a bit of hunt for glory. And in some sense it's not the worst one.

wait until people hear about research grants

> The discovery was the result of almost exactly one year of work and about $2 million of Durant’s own money

9 years ago I asked how much a Mersenne prime is worth to us. I guess we have an answer now.

https://news.ycombinator.com/item?id=10932238

> Durant, a graduate of the California Institute of Technology, found the new prime number using only publicly available unused cloud storage space.

> I was able to find this number that’s astonishingly large … but I was able to do it just by using big tech’s leftovers.

Did he do this by taking advantage of spot pricing? It isn't actually mentioned how he uses those leftovers in the article.

Heh, that's a prime example of a race condition.

Fun hypothetical, or can someone solve? How long, would this regex prime check [1] (via hn 2009) take to run on this on todays average machine?

Hitchhiker's Guide's Deep Thought "42" was 7.5 million years, just for a guide-post.

- [1] https://news.ycombinator.com/item?id=707236

This sounds like the (debunked) labor theory of value :p

https://stackoverflow.com/a/17189376/308851 claims it's O(N^2). 10^82 operations ... say you can run 10^10 iterations in a second which no current CPU is capable of but let's pretend, it's not like a factor of 10 or 100 will make a big difference given how this is like 10^54 times the age of universe.

This algorithm is not practical.

Does it? "Things are worth what people are willing to spend to get them" is a truism in capitalism and in reality.

I might be getting wooshed here.

Yikes! If so, he could have saved a lotta money by purchasing 4090s instead of spot pricing. Last time I did the math, break even between buying and renting was only 3 months. I wonder if the search took a lot longer than he anticipated

"prime" example, intended or accidental?

Isn't it basically this algorithm + overhead from using strings/regex?

  def is_prime(n):
    if n < 2:
      return False
    for i in range(2, int(n ** 0.5) + 1):
      if n%i==0:
        return False
    return True

Haven't tested this, just quickly jotted it down in the HackerNews textarea, but theoretically it should be python code, which checks if n is divisible by any number between 2 and sqrt(n).

And wouldn't this algorithm be just O(n), what does the regex engine do differently (except the string overhead)?

If I remember correctly, it is more an Austrian Economic thing than a capitalism thing, and the way I understood it, is that it is not the cost to create something that defines the value, but the price you can sell it at.

E.g, the value of the compute used was 2 million (because Durant bought it), but the prime is worthless, because he can't sell it, or use it for producing any services he can sell.

The point is, that just because something was expensive to make, doesn't mean it has a high value, and conversely (and most importantly) just because something was cheap to make, doesn't mean it isn't high value.

In life, I find a good way to value items is not what it cost to acquire it, but what it will cost to replace.

My understanding is that he used to be an engineer at NVIDIA. And while I know salaries can be quite high in the US, I didn't realize they where high enough to let you spend $2 million for a 1 year hobby project.

Fine. It's now only 10^10 times the age of the universe. much better.

This is an outlier. I met someone who was a millionaire working at Nvidia in 2018. That's not that uncommon working in tech. The stock has gone up about 30x since then. He's probably worth at least 20M if not more now. That's definitely an outlier.

Heavily depends on how sophisticated are regex engines. Regex engines are like compilers, in that they are free to do anything as long as the result doesn't change (in a certain defined manner, of course), so engines can of course specialize for that particular regex. They don't even have to specially target the non-prime regex (yes, that matches 0, 1 or n*m copies of ones where n, m >= 2) by the way, because backreferences are already pretty rare and there are lots of potential optimizations to be made if they were much more popular. So the answer can greatly vary even when we limit ourselves to contemporary libraries. That said, it would be extremely more impractical to build a string made of 2^136279841 - 1 ones to run that regexp.

(Seriously though, it would make a very good April fools' day PR to recognize that particular regex and trigger a non-trivial prime check routine to match them.)

Here N should be interpreted as the number itself, not the number of digits (in any base). So the actual complexity is exponential in terms of the number of digits and in fact it will take about 10^(10^8) times the age of universe to build the string alone.

Once physical hardware is involved, the problem gets a lot more complicated.

If you're talking about $2M worth of 4090s you have to concern yourself not only with putting them in hosts, but also with adequate space, power distribution, cooling, and networking. You have to figure out how to gracefully handle hardware failures. You have to install operating systems, or at least come up with some mechanism to deploy automatically. And you just straight up have to supply labor to get 1000+ of these things plugged in.

All that before you can get even get to the "fun part". If you're a multi-millionaire you might be willing to just pay the spot price premium.

Yeah I’m totally fine with him spending his money on whatever hobby he likes, but the message is just strange, this and the other message that “he wants [GPUs] to be used for research and discovery”. And donating the $3k prize money to his high school to advance math and science education after burning $2m… It’s obviously still a nice thing, but why would you even mention it…

That said, maybe he felt pressured to give the reporter more than “I was just having fun”.

Luke didn't just work at NVIDIA. He spent over ten years there and was, for a while, one of the CUDA architects.

That's fair. I suspect that if we had an efficient market for prime numbers, a coalition would have paid ~$2M for someone to calculate this number. He can't sell it because he didn't bother to create a market for it.

>In life, I find a good way to value items is not what it cost to acquire it, but what it will cost to replace.

I completely agree with this.

Naw the dude had a year. It's not that hard to pay 1 contractor $30/hr to set up PXE boot, assemble machines and GPUs, air handling units, GPUs, and electrical sub panels. I've done a similar "jack of all trades" job for a weed company in Oakland way back before I became a software engineer. 1000 GPUs only takes 2 weeks to deploy.

I highly doubt the effort to find this prime number will be worthy of peer reviewed publication

> but the prime is worthless, because he can't sell it, or use it for producing any services he can sell.

You are talking about him. He is on wikipedia / history forever at least as a footnote whenever you google progression of prime discoveries. If he wants to start some consulting business he is the "guy that discovered the big prime", and so on. This is absolutely something he can bank on down the line, it's weird to call it worthless. Those are things that some people with way more than $2m would probably pay for, they just can't do it.

Oh.

It's really not practical.