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## Nicholas Sze of Yahoo Finds Two-Quadrillionth Digit of Pi299

gregg writes "A researcher has calculated the 2,000,000,000,000,000th digit of pi — and a few digits either side of it. Nicholas Sze, of technology firm Yahoo, determined that the digit — when expressed in binary — is 0."
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## Nicholas Sze of Yahoo Finds Two-Quadrillionth Digit of Pi

• #### an so are an infinite other digits in that number (Score:2)

an so are an infinite other digits in that number

• #### Re:an so are an infinite other digits in that numb (Score:4, Funny)

by Anonymous Coward on Thursday September 16, 2010 @05:58PM (#33605554)
Word. This discovery is useless. Now, if he'd managed to prove that the digit, when expressed in binary, is 2... That'd be something to shout about!
• #### Re: (Score:3, Insightful)

does this bit from TFA strike anyone else as a bit odd?

"The computation took 23 days on 1,000 of Yahoo's computers, racking up the equivalent of more than 500 years of a single computer's efforts."

So.... 1000 machines, 23 days, assuming embarrassingly parallel that's 23000 days of computation on 1 machine.

23000/365 = 63.0136986 years

now each of those could have 8 cores and they meant 500 years on a single core processor of course.
but still odd phrasing.

• #### Re:an so are an infinite other digits in that numb (Score:5, Funny)

on Thursday September 16, 2010 @07:51PM (#33606408)

The computation took 23 days on 1,000 of Yahoo's computers, racking up the equivalent of more than 500 years of a single computer's efforts.

And before answering, the computer paused and said, "You're not going to like it ..."

• #### Re: (Score:3, Insightful)

by jd (1658)

You're forgetting all the zombie networks that connect to Yahoo. There's probably a few billion nodes there, and there's not a friggin' chance Yahoo will admit to knowing about them.

• #### Re: (Score:3, Informative)

The thing that I find funny, is that had they used the Bailey-Borwein-Plouffe formula, [wikipedia.org] they could have saved themselves some very considerable computing resources.
• #### Re:an so are an infinite other digits in that numb (Score:5, Funny)

on Thursday September 16, 2010 @06:13PM (#33605716) Journal

the digit -- when expressed in binary -- is 0.

Amazing, so is Yahoo's profit projections within five years!

• #### Oh yeah? (Score:5, Funny)

on Thursday September 16, 2010 @05:42PM (#33605380)

Well, the 243,000,500,000,000,000,002th digit of pi is "4".

Go on, prove me wrong.

• #### Re:Oh yeah? (Score:4, Funny)

on Thursday September 16, 2010 @06:02PM (#33605608) Journal

No it's not. Because I say so.

(See, I have a 90% chance of being right and you have a 10% chance of being right, so I win Monte Carlo testing, and I provided more evidence than you, so I win in a civil suit.)

• #### Re: (Score:2)

Well, the 243,000,500,000,000,000,002th digit of pi is "4".

Go on, prove me wrong.

I can't readily disprove your theory, but I can disprove your grammar in that the 243,000,500,000,000,000,002th digit of Pi should in fact be the 243,000,500,000,000,000,002nd digit of Pi.

• #### You fail math forever (Score:5, Funny)

on Thursday September 16, 2010 @05:44PM (#33605424)

the digit - when expressed in binary - is 0.

*facepalm* So that's 9 in decimal, right?

• #### Re: (Score:2, Informative)

What they should have said is: The two quadrillionth digit in the binary expansion of pi is 0.

Is it?

• #### Re: (Score:2)

Agreed. Let's look at the exact phrasing.

A researcher has calculated the 2,000,000,000,000,000th digit of pi [...] the digit – when expressed in binary – is 0.

"Digit" without qualification usually means decimal digit. So presumably, he found the two quadrillionth decimal digit, which, in binary, is 0. Let me just convert that to decimal...

*uses calculator*

Apparently that's equivalent to 0.

• #### Re:You fail math forever (Score:4, Funny)

by jd (1658) <imipak@yah[ ]com ['oo.' in gap]> on Thursday September 16, 2010 @06:38PM (#33605916) Homepage Journal

Are you sure? 0, for large values of 0, approaches 1, for small values of 1.

• #### Re: (Score:2)

No. [hmc.edu] It is easier to convert 16bit into binary than decimal system.
• #### Re: (Score:2)

Why do people keep saying digit and being ambiguous? It's called a bit. The two quadrillionth bit.

• #### Re: (Score:2)

I suppose if the calculation was in hex we would talk about the Nth nibble.

• #### Re: (Score:2)

I don't get it. What does 9 have to do with anything?

• #### Re: (Score:2)

the digit - when expressed in binary - is 0.

*facepalm* So that's 9 in decimal, right?

Yeah, that's just fucking terrible. Honestly I'm getting so sick of people writing terrible, terrible blog postings on supposedly high tech blogs. If this were a cat blog, I would understand, but its just silly for slashdot to post such crap. Why does this happen?
-Taylor

• #### Re: (Score:2, Funny)

Yeah, I've seen more credible technical journalism on the blog the guy at the yarn museum does.

Told you I'd use it.

• #### If zero equals nothing then... (Score:4, Funny)

on Thursday September 16, 2010 @05:46PM (#33605436)
...move along people, nothing to see here.
• #### Put to good use (Score:5, Funny)

by Anonymous Coward on Thursday September 16, 2010 @05:46PM (#33605440)

Good to know they're putting those idle datacenters to good use. It's not like Yahoo has any real users anymore to generate load.

• #### Last Digit? (Score:5, Funny)

on Thursday September 16, 2010 @05:47PM (#33605450)

"Interestingly, by some algebraic manipulations, (our) formula can compute pi with some bits skipped; in other words, it allows computing specific bits of pi," Mr Sze explained to BBC News.

So why don't they just use their formula to compute the last digit of Pi already?
That would be the rational approach. Who cares about the two quadrillionth digit??

• #### Re:Last Digit? (Score:4, Funny)

on Thursday September 16, 2010 @05:53PM (#33605512) Homepage Journal

Irrational numbers care not for your "rational approach".

• #### Re: (Score:2)

That would be the rational approach. Who cares about the two quadrillionth digit??

I see what you did there.

• #### Re: (Score:2)

by jd (1658)

The last binary digit of Pi is both 0 and 1.

• #### Re: (Score:2)

No. It is only 1. The last digit of any binary mantissa will always be 1.

• #### In binary? (Score:5, Funny)

on Thursday September 16, 2010 @05:51PM (#33605502)
Geez, even I could have gotten it right half the time.
• #### how do they do it (Score:2)

2,000,000,000,000,000 digits takes about from 200 TB (binary digits) to 3600 TB (hexadecimal digits).

So, do you have to keep the whole number in the memory to calculate some more digits? Or can you keep the whole thing on the hard disk because it is not needed to calculate more digits?

If the first is the case, how do they do it? It is more than 100 hard disks worth of memory, who has that?

If the second is the case, why don't they just calculate the digits from wherever the last record ended...

• #### Re: (Score:3, Informative)

Regardless of what actually happened, there isn't any computation that requires keeping data in memory rather than hard disk. Memory is just faster, if you need more space for the computation, you can always actually use the 100 disks.

• #### What are the odds? (Score:5, Funny)

on Thursday September 16, 2010 @06:00PM (#33605582)

the digit — when expressed in binary — is 0.

Jeez, what are the odds of that?

• #### Re: (Score:3, Insightful)

Apparently, 100%. :D
• #### Re: (Score:2)

gotta be a 1 in a million chance that, of all the numbers it could be... that it'd be zero!

• #### Re: (Score:2)

Well 50% chance if your zero is binary or 10% chance if your zero is decimal. Good thing the article let us know ;). Or you can't really ask that question if it isn't a value that ever changes, ever. Or maybe you can. Probably.

Off chance (no pun intended) does anybody know if the decimal number distribution for pie breaks out to an equal distribution for numbers 0-9? Because that off-chance might changes things, probably. Crumb size is important.
• #### Re: (Score:3, Insightful)

the digit — when expressed in binary — is 0.

Jeez, what are the odds of that?

1 in 10

The interesting thing about this article is how they calculated the digits. They broke the problem up into small pieces and had them calculated in parallel. This approach isn't something that's new or all the unique, but what is is applied to is. Most mathematical calculations are done in a near linear fashion, not in parallel. So for them to be able to do this is a big step forward in how we approach these types of problem in the future.

Of course I'm very interested in this since it seems I'll be doin
• #### Re: (Score:3, Informative)

The interesting thing about this article is how they calculated the digits. They broke the problem up into small pieces and had them calculated in parallel. This approach isn't something that's new or all the unique, but what is is applied to is. Most mathematical calculations are done in a near linear fashion, not in parallel. So for them to be able to do this is a big step forward in how we approach these types of problem in the future.

At least with regards to calculating Pi, it's isn't particularly new.

• #### A serious question (Score:4, Interesting)

on Thursday September 16, 2010 @06:05PM (#33605648)
I've always wondered about these ridiculously precise values of pi - doesn't that imply a measurement (of circumference or diameter) smaller than the Planck length? What's the point of 2 trillion decimals of precision?
• #### Re: (Score:2)

Because it's there. Also, everyone with a third-grade education knows what pi is, so it's useful for popularization of science.

• #### Re: (Score:3, Interesting)

Well, the radius of the visible universe is roughly 7.6 * 10^6 Planck lengths [google.com]. That means the volume is on the order of 10^183 cubic Planck lengths. So, if you can calculate PI to 200 digits or so, you're really accurate. At some point, more accurate than spacetime itself.
• #### Re: (Score:3, Interesting)

So obviously, 640 digits of pi should be enough for anybody.

And here they are:

• #### Re: (Score:2)

It proves he had access to more useless cpu cycles than anyone else. A 'mine's bigger' sort of competition, if you know what I mean, and if you don't, seriously, what are you doing here?

• #### Re:A serious question (Score:4, Funny)

on Thursday September 16, 2010 @11:23PM (#33607426)

A 'mine's bigger' sort of competition,

Would that be diameter or circumference?

• #### Re: (Score:2)

Just tried this. Calculated the circumference of a circle with a radius of 1 meter using Pi to 7 digits (3.1415926) and using Pi to 100 digits. The discrepancy is around 1.0718 * 10^-7m, or around 107 nanometers. That's quite a small discrepancy, and even many scientific calculators will have a more precise value of Pi. By using 10 digits instead of 7, the discrepancy falls to 1.795 * 10^-10m, taking it into picometer range. Granted, this is not Planck length range, but goes a long way to show that yeah, qu
• #### Re: (Score:3, Insightful)

Pi has the property that all binary strings of a given length occur with equal frequency, making it an excellent source of fair pseudorandom bits. There are plenty of applications in which 2 quadrillion pseudorandom bits is grossly insufficient.

• #### Re: (Score:3, Funny)

point? there is just one point when you're a pi value researcher.
• #### Bailey–Borwein–Plouffe formula (Score:3, Interesting)

on Thursday September 16, 2010 @06:05PM (#33605650)

Bailey–Borwein–Plouffe formula [wikimedia.org] lets you calculate the n-th digit of pi without calculating the n-1 digits.

I wonder what formula was used to calculate the digit here.

• #### Confirmation ? (Score:3, Insightful)

on Thursday September 16, 2010 @06:13PM (#33605710)

And, we know this is correct how ?

• #### Re:Confirmation ? (Score:4, Funny)

on Thursday September 16, 2010 @06:17PM (#33605742) Homepage Journal

Netcraft.

• #### Re: (Score:2)

Beyond having proven the algorithm, and verifying the implementation of the algorithm on known digits of pi, we do not and will not.

• #### Re: (Score:2, Funny)

They asked some autistic dude who has it memorised to 3 quadrillion digits and he said "yes"

• #### Best article (Score:2)

This article [radionz.co.nz] actually explains it better, and uses the phrase "piece of pi". I love it.

• #### Fuzzy Math (Score:2)

Does Fuzzy Math have a hair-pi?
• #### Uh, so what? There are an infinite number of them (Score:2)

just as there are an infinite number of primes. It's not like the 2,000,000,000,000,000th digit of pi is any more significant than say the 200th. At least with primes you reduce the time for factorization.

• #### Re:Uh, so what? There are an infinite number of th (Score:4, Funny)

on Thursday September 16, 2010 @06:41PM (#33605938) Homepage Journal

It's actually 13 orders of magnitude less significant than the 200th.

• #### Re: (Score:2)

It's actually 13 orders of magnitude less significant than the 200th.

Yeah, I knew some smart ass would say that. I almost didn't use the word "significant" but the meaning of the word is ambiguous. So we are both right.

• #### Re: (Score:2)

the meaning of the word is ambiguous. So we are both right.

Also, you're both wrong.

• #### Re: (Score:2)

I was hoping for a funny rather than the informative I got, to be honest.

• #### Re: (Score:2)

just as there are an infinite number of primes. It's not like the 2,000,000,000,000,000th digit of pi is any more significant than say the 200th. At least with primes you reduce the time for factorization.

Actually finding large primes has very little to do with factorization. In general, the most efficient factorization procedures, the elliptic curve sieve and the general number field sieve http://en.wikipedia.org/wiki/Number_field_sieve [wikipedia.org] don't benefit from knowing any primes in advance beyond a few very small primes. Moreover, the largest primes known are all of special forms that don't show up very often. For example, the very largest primes are known as Mersenne primes which are primes which are 1 less tha

• #### Re: (Score:2)

just as there are an infinite number of primes. It's not like the 2,000,000,000,000,000th digit of pi is any more significant than say the 200th. At least with primes you reduce the time for factorization.

Actually finding large primes has very little to do with factorization. In general, the most efficient factorization procedures, the elliptic curve sieve and the general number field sieve http://en.wikipedia.org/wiki/Number_field_sieve [wikipedia.org] don't benefit from knowing any primes in advance beyond a few very small primes. Moreover, the largest primes known are all of special forms that don't show up very often. For example, the very largest primes are known as Mersenne primes which are primes which are 1 less than a power of 2. We can determine if such numbers are prime using a very efficient test called the Lucas-Lehmer test. The largest such prime known today is 2^43,112,609-1. This is much, much larger than any number we'd want to practically factor (for example numbers used in RSA encryption are generally on the order of a few hundred digits. It is believed that numbers with 2000 or so digits will be secure for the indefinite future). So yeah, finding large primes is about as useful as this when it comes to practical factoring. There are other somewhat good reasons to be interested in finding large primes, but factoring isn't one of them.

Yeah, I know all of that. That wasn't my point. Reread what I wrote.

• #### Re: (Score:2)

Ok. Reread it. Now confused. What did you mean when you said "At least with primes you reduce the time for factorization"?

• #### What, not a relational database? (Score:2)

The horror, they used map reduce instead of a acid compliant database server.

• #### fine, and I have calculated the last digit of pi. (Score:4, Insightful)

on Thursday September 16, 2010 @07:14PM (#33606196)

It is 1 in binary.

• #### Probability of 50% (Score:2)

And I have calculated that if he is incorrect and the value is one and not zero that I have a 50% chance of being correct.

Computer programmers do it byte by byte.

Working...