Pi Calculated to 105 Trillion Digits. (Stored on 1 Petabyte of SSDs) (solidigm.com) 95
Pi was calculated to 100 trillion decimal places in 2022 by a Google team lead by cloud developer advocate Emma Haruka Iwao.
But 2024's "pi day" saw a new announcement... After successfully breaking the speed record for calculating pi to 100 trillion digits last year, the team at StorageReview has taken it up a notch, revealing all the numbers of Pi up to 105 trillion digits! Spoiler: the 105 trillionth digit of Pi is 6!
Owner and Editor-in-Chief Brian Beeler led the team that used 36 Solidigm SSDs (nearly a petabyte) for their unprecedented capacity and reliability required to store the calculated digits of Pi. Although there is no practical application for this many digits, the exercise underscores the astounding capabilities of modern hardware and an achievement in computational and storage technology...
For an undertaking of this size, which took 75 days, the role of storage cannot be understated. "For the Pi computation, we're entirely restricted by storage, says Beeler. "Faster CPUs will help accelerate the math, but the limiting factor to many new world records is the amount of local storage in the box. For this run, we're again leveraging Solidigm D5-P5316 30.72TB SSDs to help us get a little over 1P flash in the system.
"These SSDs are the only reason we could break through the prior records and hit 105 trillion Pi digits."
"Leveraging a combination of open-source and proprietary software, the team at StorageReview optimized the algorithmic process to fully exploit the hardware's capabilities, reducing computational time and enhancing efficiency," Beeler says in the announcement.
There's a video on YouTube where the team discusses their effort.
But 2024's "pi day" saw a new announcement... After successfully breaking the speed record for calculating pi to 100 trillion digits last year, the team at StorageReview has taken it up a notch, revealing all the numbers of Pi up to 105 trillion digits! Spoiler: the 105 trillionth digit of Pi is 6!
Owner and Editor-in-Chief Brian Beeler led the team that used 36 Solidigm SSDs (nearly a petabyte) for their unprecedented capacity and reliability required to store the calculated digits of Pi. Although there is no practical application for this many digits, the exercise underscores the astounding capabilities of modern hardware and an achievement in computational and storage technology...
For an undertaking of this size, which took 75 days, the role of storage cannot be understated. "For the Pi computation, we're entirely restricted by storage, says Beeler. "Faster CPUs will help accelerate the math, but the limiting factor to many new world records is the amount of local storage in the box. For this run, we're again leveraging Solidigm D5-P5316 30.72TB SSDs to help us get a little over 1P flash in the system.
"These SSDs are the only reason we could break through the prior records and hit 105 trillion Pi digits."
"Leveraging a combination of open-source and proprietary software, the team at StorageReview optimized the algorithmic process to fully exploit the hardware's capabilities, reducing computational time and enhancing efficiency," Beeler says in the announcement.
There's a video on YouTube where the team discusses their effort.
The old record was going to be broken ... (Score:4, Funny)
... as soon as someone got around to it.
Quantum limits? (Score:2)
Don't you run into quantum limits at some point where the circle can no longer be perfectly circular causing further precision in Pi to fail to reflect the actual object?
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The real question is how many library of congress would the 105 Trillion Digits print out be if printed? We need numbers we can put in perspective.
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According to Wolframalpha, if printed, all those digits would take 23.58 billion pages. I don't know what is the average number of pages in a book, but assuming 300 would be reasonable. You'd get 78.6 million books. The Library of Congress has 173 million items, of which 41.36 million may considered volumes of the size of book (25.49 book + 15.87 other bounded material). Altogether, all those digits are shy of two Libraries of Congress.
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Thanks a lot! I couldn't sleep since I asked the question in my OP. I might be able to sleep tonight, thanks again!
Re: Quantum limits? (Score:2)
Couldn't they have done this in an RPi? I mean, it must have occurred to them at some point in this project...
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Your issue is whether our Euclidean geometry model is an accurate representation of the world around us. You may or may not be correct in thinking that quantum mechanics implies that space comes in "discrete" lumps when you get down to the Planck distance, but p
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circles can be perfect
Mathematically, sure. They mean of a physical object.
Your issue is whether our Euclidean geometry model is an accurate representation of the world around us.
That was not their issue. They are just claiming that past a few dozen digits that the precision doesn't increase the accuracy of the outcome.
I'd argue that even for theoretical math, a few hundred digits is the limit of anything we'd need to actually use for anything besides verifying other math to the same precision.
Re:Quantum limits? (Score:5, Interesting)
If you had the diameter of the known universe measured in quark widths, and you wanted to know its circumference, you'd only need around 44 digits of pi.
That's the most digits we can ever use for practical things.
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Thank you. That was my question and you answered it.
Cumulative errors (Score:3)
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That's the most digits we can ever use for practical things.
All practical things are made of infinities of impractical things. Those infinities need somewhere to live. After the first 44 digits of Pi is great place for them.
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Spoiler alert (Score:4, Funny)
The last digit is zero.
Re:Spoiler alert (Score:5, Funny)
Hey! I was still reading this!
What the heck is wrong with rounding? (Score:1)
Re:What the heck is wrong with rounding? (Score:5, Funny)
It's completely irrational. Pi should be a round number.
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Ahem, in Indiana it is? [wikipedia.org]
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you can store numbers on any kind of hard drive (Score:2)
> "These SSDs are the only reason we could break through the prior records and hit 105 trillion Pi digits
I find this claim suspicious.
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Yeah they could pipe it to /dev/null for all it matters
The limit is storage? (Score:5, Funny)
Why don't they just use compression?
/s [for those who need it]
Re:The limit is storage? (Score:4, Informative)
It's pretty easy to compress:
Integral from -1 to 1 of (1/sqrt(1 - x^2)) dx.
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Compression is overkill.
I would just sort the decimal digits and count the runs manually.
Should look something like this when it's done:
digit | count
0 | 10500000000000
1 | 10500000000000
2 | 10500000000000
3 | 10500000000000
4 | 10500000000000
5 | 10500000000000
6 | 10500000000000
7 | 10500000000000
8 | 10500000000000
9 | 10500000000000
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Apparently they were using some kind of expansion. I don't know why you'd need that much more (10x !?) than 105 terabytes to store 105 trillion digits, and that's if you're storing each base-10 digit using 8 bits, which is already an "expansion".
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You've got to show your work in math class.
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Arguable the best compression you'll ever get is 1 x pi lol
Editors (sigh) (Score:2)
Contrary to TFS title, "(Stored on 1 Petabyte of SSDs)" is not "used 36 Solidigm SSD" (which hold a petabyte of data). One petabyte of SSDs would (probably) fill a few Library of Congresses -- in which case that unit could simply be used. :-)
What's so special about pi? (Score:1)
Any irrational number will do. How about e or root 2? I bet the 105 trillionth digit of 1/3 is 3 but I'd like to see you prove it. OK you can probably do that without actually doing the calculation since it is a repeating decimal.
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Would a random number generator be quicker?
Irrational doesn't imply that it's difficult (Score:5, Informative)
0.121121112111121111121111112... is irrational, but I can tell you with just some quick calculations that the 150,000,000,000,000th digit is 1. (The 150,000,007,349,285th digit is the next 2.)
Re: What's so special about pi? (Score:3)
You might want to take a look at the differences between rational, irrational, and transcendental numbers. Pi is transcendental, not merely irrational.
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"The first number to be proven transcendental without having been specifically constructed for the purpose of proving transcendental numbers' existence was e, by Charles Hermite in 1873." https://en.wikipedia.org/wiki/... [wikipedia.org]
It was literally the first alternative mentioned in the GP
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They aren't the ones that decided it's special. I never hear about anyone memorizing even a dozen digits of e. Pi is a much simpler concept and and you want to generate headlines people will make note of. Especially if what you're doing has no practical application.
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Calculating e is pretty boring: the Taylor series converges extremely fast. You can calculate e by hand to 100dp on a single sheet of paper and have space left over. sqrt 2 is also pretty boring: Newton-Raphson. The choice of pi is pretty arbitrary, but it has a wealth of interesting approaches to calculate it.
Now recite (Score:2)
Now recite by memory.
Is it searchable? Where does it contain 314159265? (Score:3)
I presume Pi contains little recursive Pi's of differing lengths, is the longest one in 10^12 digits about 12 digits? What digit does it start at?
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What's the first prophet's name that appears in base-10 ASCII? (Let's settle this)
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I presume Pi contains little recursive Pi's of differing lengths, is the longest one in 10^12 digits about 12 digits? What digit does it start at?
How deep is the 256x256 array of 1’s and 0’s that form an ascii art circle?
Contact (Score:2)
"How deep is the 256x256 array of 1’s and 0’s that form an ascii art circle?"
Wasn't that in base eleven?
Is Ann Druyan still alive?
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The Pi search engine only looks at the first 200 million digits.
https://www.angio.net/pi/ [angio.net]
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Thanks! "The string 31415926 occurs at position 50366472. This string occurs 3 times in the first 200M digits of Pi."
After a certain point (Score:4, Informative)
After a certain point, they could fill drives with the output of a real random number generator? Who's gonna check?
Ha-hah, only serious; but there's actually a really good answer for this. There is an algorithm for finding the Nth digit of Pi, and it's *fast*, not requiring you to compute previous digits. Thus, spot-checking the data for accuracy is very doable.
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"There is an algorithm for finding the Nth digit of Pi,"
So what is the Googol-factorialth digit of Pi?
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7, but I can't tell you how I know. Feel free to verify.
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Are there also algorithms to find the Nth digit of other transcendent numbers, like e?
I guess yes. But never expanded my math deep anough.
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Cool! Thanks for the link!
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Every article that isn't about AI or crypto or a new superhero movie franchise is a blessing.
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OK, let me quickly make this about crypto as well:
Everyone complains about crypto being a power guzzler, but somehow this project mentioned here is fine.
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I'm going to plagiarize the OP but it seems apropos:
Who gives a shit.
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pretty sure the debt is more than $1.05
Afraid (Score:2)
What for? (Score:3)
The errors from rounding it up to 1000 digits or thereabouts are probably small enough to allow the circumnavigation of the known Universe.
Re:What for? (Score:4)
Quite a few scientists have shown that Pi to the 39th digit is accurate enough to describe the circumference of the known universe (~14 billion light years) to the accuracy of the width of a hydrogen atom. The observable universe down to the distance of the electron orbit of a hydrogen atom? I think 39 digits is good enough for anything we can reasonably need to measure.
https://www.jpl.nasa.gov/edu/n... [nasa.gov]
Re: What for? (Score:2)
Ah, but we can do better. 63 digits of pi are good enough to specify any location in the known universe to within a planck length. Much better than the comparatively huge hydrogen atom.
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Okay. So, the trillion digits are even less useful.
Very precise representation of Pi! (Score:3)
I use a form of compression that stores Pi in a handful of bytes: U+03C0
Pi comes up a lot in mathematics, and you can manipulate the symbol with algebra and sometimes eliminate it in the final equation. That's harder to do if you use the fully expanded 1 petabyte version of Pi.
Had to say it (Score:2)
We're gonna need a bigger can of whipped cream.
Day after Pi Day is Ides of March (Score:2)
Instead of stabbing Caesar, The Aristocrats could have hit him with left over pies. Except the Romans didn't celebrate Pi Day because their value for Pi was III.
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Their value of PI was most likely 22 / 7 or 355 / 113, as since the previous 3000 years of other cultures.
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22/7 isn't even accurate to 10 digits.
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It's possible to halve the storage, store each number in 4 bits, for two digits per byte. I suspect that there's a way to reduce that even further.
So useful! (Score:2)
is it really an achievement? (Score:2)
the exercise underscores the astounding capabilities of modern hardware and an achievement in computational and storage technology
That would have flied 25 years ago, but in the last several years we have the progress of things like AlphaFold, generative AI, LLMs and other advances in machine learning that demonstrated how this progress resulted in practical revolution.
The effort in computing Pi digits seems anachronistic and simply misplaced, impressing only a handful of aged fanboys still nostalgically re
But have they found the Message? (Score:2)
Eleanor "Ellie" Arroway was convinced there was a Message stored in Pi.
(True nerds will know the novel.)
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Every novel that's every been written is contained in pi. The problem is finding it.
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I believe it is not known (mathematically) whether that is true.
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That chapter ruined the entire book.
Pi is random so if you go out far enough you'll find every message.
Ellie found a message from God because that's what she was looking for. She discarded everything that had brought her to where she was and threw away enlightenment. Which is not to say that a search for a Creator is incompatible with enlightenment - perhaps the opposite is more true - but she deceived herself.
A hopeful story that wraps up with a tragedy and a downfall for no good reason.
The movie did the
Circle? (Score:2)
Have they proven that PI actually is the algorithm they use to calculate the value?
I mean the diameter times PI is the circumference. But how do you prove that the algorithm checks out to that in any meaningful way?
Or have they redefined the value of PI to being what the current algorithm produces?
Will my circles be rounder?!?!
What a waste of ressources (Score:2)
These researchers should be defunded... Oh, wait, this is not research. This is a fucking publicity _stunt_!
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Ah, no. Pi is irrational and that is _proven_ (since 1760, no less). This is a stunt, nothing else.
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1_{\pi} (Score:1)
Great (Score:2)
Now I have to start my circle all over again to the new spec.
and... (Score:2)
And, the point being... well, nothing.
Posted ... (Score:2)
You had one job ...
Amusing, but... (Score:2)
Amusing... and I confess to have been rather infatuated with Pi in my youth. But realistically, you need very few digits of pi. Even NASA only uses pi down to 15 digits. 62 digits is enough to make a perfect circle the size of the known universe down to the Plank length.
Who's going to confirm they got it right? (Score:2)
And how?
Now what to do... (Score:2)
with all those digits?
I struggle... (Score:2)
I struggle to identify a practical use of the value of Pi beyond 1 trillion digits/decimal places...
In my realm, 3.14159263 has sufficed, but I guess someone, somewhere, has a practical use for, let's say, Pi to say 50 or 100 digits.