## Nicholas Sze of Yahoo Finds Two-Quadrillionth Digit of Pi 299

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."*
## 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)

## 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)

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)

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)

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

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

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

The hexadecimal digit extraction formula for PI (that allows you to skip calculating the previous hex digits) is already known. It can calulcuate the N'th hexadecimaldigit of Pi without calculating most of the previous digits: http://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula [wikipedia.org]

A slower generalized version that can extract the n'th digit of Pi in any base (including decimal) has also been found: http://web.archive.org/web/19990116223856/www.lacim.uqam.ca/plouffe/Simon/articlepi.html [archive.org]

## Oh yeah? (Score:5, Funny)

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)

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

243,000,500,000,000,000,002thdigit of Pi should in fact be the 243,000,500,000,000,000,002nddigit of Pi.## Re: (Score:3, Funny)

## Re: (Score:3)

I couldn't care more!

?

## Re: (Score:2)

I might or might not care - but only if you don't know which.

## Re: (Score:3, Insightful)

docare, right? I mean, since you just said it is possible for you to care less than you do. I'm just sayin'... Just for your edification, the proper way to say what you are trying to say is, "I could not care less." And with regard to the subject at hand in this thread, the idea that someone's poor English skills could have any bearing whatsoever on his or her skills at mathematics is just laughable and shows how little anyone presuming su## Re: (Score:2)

Really? You "could care less"?I always read that as a threat. "I

couldcare less... so don't push me!"## Consistency, and relative caring (Score:2, Flamebait)

The attention to detail one pays in one field of endeavor is somewhat of an indicator of how much attention to detail one pays overall. Sure, your defense is the SAT separates the two, but the brain doesn't work on different problem classes completely independently!

There are two ways to express uncaring: "I could not care less", meaning I care as little as possible for this thing, in fact it is not possible for me to care any less than I do right now.

Then there's the somewhat intricate (for minds like your

## Re:Oh yeah? (Score:5, Funny)

## Re: (Score:2)

People never complain about mad scientists lacking control groups.

## Re: (Score:3, Funny)

You can't handle the 2th!

## Re: (Score:2)

In other words, the proof wasn't valid? Watch, I can do the same thing:

Many hills are green. Therefore, the "infitieth" (???) digit of Pi is 27. QED.

## Re: (Score:2)

You call that 'somewhat' bizarre? Marginally bizarre at best. Where are the pink unicorns?

## Re: (Score:2)

They fell off the graph hole.

## Re: (Score:2)

## Re: (Score:2)

In base 28, yes.

## Re: (Score:2)

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

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

## Re: (Score:2, Informative)

## Re: (Score:2)

Is it?

They aren't clear about that.

## 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)

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

## Re: (Score:2)

Modern mathematiciansIf you're using 0, you're a modern mathematician, and not one of those Roman-numeral types.

## Re: (Score:2)

## 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)

*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.

## Re: (Score:3, Informative)

101-5

110-6

111-7

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

## Put to good use (Score:5, Funny)

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)

"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)

Irrational numbers care not for your "rational approach".

## Re:Last Digit? (Score:4, Informative)

Pi is NOT irrational! It is transcendental. Look it up!

http://en.wikipedia.org/wiki/Transcendental_number [wikipedia.org] :

All real transcendental numbers are irrational, since all rational numbers are algebraic.

## Re: (Score:2)

That would be the

rationalapproach. Who cares about the two quadrillionth digit??I see what you did there.

## Re: (Score:2)

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)

## 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)

the digit — when expressed in binary — is 0.Jeez, what are the odds of

that?## Re: (Score:3, Insightful)

## 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)

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 (Score:2, Interesting)

Of course I'm very interested in this since it seems I'll be doin

## Re: (Score:3, Informative)

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

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

## 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)

## Re: (Score:3, Interesting)

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

And here they are:

http://www.eveandersson.com/pi/digits/pi-digits?n_decimals_to_display=640&breakpoint=100 [eveandersson.com]

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

That's a rather ... odd ... reaction to my post. You're hoping to eliminate my superior genes so we don't wipe you out?

## Re: (Score:2)

## 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)

A 'mine's bigger' sort of competition,

Would that be diameter or circumference?

## Re: (Score:2)

## 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)

## Bailey–Borwein–Plouffe formula (Score:3, Interesting)

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)

And, we know this is correct how ?

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

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)

## 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)

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)

## Calculated? (Score:2, Funny)

## 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)

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.

## Re: (Score:2, Funny)

## Re:So, what is the digit in decimal? (Score:4, Funny)

It is, but it's encoded in UTF-35, not ASCII.

## Re: (Score:2)

Already done:

http://en.wikipedia.org/wiki/The_Neverending_Story [wikipedia.org]

## Re: (Score:3, Funny)

Or perhaps convert it to ASCII to see if pi actually represents a story of some kind that is being told to us by the aliens.

You know that's the revelation at the end of a sci-fi novel by a certain revered astronomer, right?

Say 'gain?

## Re: (Score:3, Informative)

We only know how to calculate it in binary (or any base that is a power of 2). You can't convert to decimal without know all the rest of the digits.

## Re:So, what is the digit in decimal? (Score:5, Informative)

We only know how to calculate it in binary (or any base that is a power of 2). You can't convert to decimal without know all the rest of the digits.

Parent is correct, digits of pi can be calculated independently in base 2, 4, 8, 16 or 2^n since the 1990s [maa.org]. So, it is possible to calculate the 2,000,000,000,000,000th number of pi without calculating the digits before that one. Now, if we want to calculate the digit in decimal (or converse the binary digit to decimal), we need to calculate all of the two-quadrillion digits. Knowing this digit is in itself not very interesting.

## Re: (Score:2)

BTW, the link I provided is to an article about Bailey's formula.

## Re: (Score:2)

Replied to wrong thread! Sorry.

## Re: (Score:2)

## Re: (Score:3, Insightful)

I can calculate it completely in base pi: 10.0 done. What's all the fuss about? You just need to be smarter when picking your bases and you can avoid all this trouble.

## Re: (Score:2)

Yeah, given their slides, I'm surprised they're not introduced as, "Advertising Brokerage firm, Yahoo!"

## Re: (Score:3, Funny)

Well, it will help to date the story to this year, compared to stories that run in 2012 that will say 'defunct technology firm yahoo ...'

## Re: (Score:2)

If he's wrong i'll take the prize for saying it's 1