Here's an interesting item: Fabrice Bellard has computed 2,699,999,990,000 decimal digits of π on a single desktop computer, beating records previously held by supercomputers.
The computation took about 131 days, and beats the previous record of 2,576,980,370,000 decimal digits.
Speaking of π, this interesting page lets you search for patterns in the first 200 million digits of π. For example, 00000000 appears for the first time at "position 172,330,850 counting from the first digit after the decimal point".
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12 comments:
I have never quite understood what this achieves. Sure, it demonstrates use of different methods to calculate pi & shows how cheap computing resources have got. But that level of accuracy is never ever required for any mathematical application. At the most, 10 significant digits is enough
Who will be the first to calculate the first 3,141,592,653,589 decimal places, I wonder? :-)
in response to Anon, if practical application is your concern, reading the blog of a theoretical computer scientist may not be in your best interests.
just sayin' :)
Would be possible to create something like a data basis of π, to allow that when people tried to calculate π's decimal cases, they could start from a very big number of them, instead of starting from scratch? I don't know if that makes sense with the methods computers use, just asking.
The pi search page is wonderful. Those with no mathematical interest would just find it monumentally absurd. I've known about this site for a while. I sent the url to my guitarist pal Chris Newman whose website start page has something like "if you find this music interesting click here and if not click HERE"- the second option taking you to a page of bus timetables for Scunthorpe or similar tedium. He used the pi site for a while....
I remember reading a long time ago when a certain mathematician discovered he was able to identify the Xth digit of pi WITHOUT having to first identify the (X-n)th digit. (X is a large number; n is a small number.) I'd like to check that out again; it's most intriguing to me.
Fabrice Bellard has computed 2,699,999,990,000 decimal digits of π
Any idea why not 2,700,000,000,000 digits? It can't be that hard to compute 10,000 more digits. I don't know whether the weird number is for humorous effect, or whether there's a good reason.
Miranda:
You're talking about the Bailey-Borwein-Plouffe algorithm. Sometimes it is described like the way you have, but this is somewhat misleading, since there is no rigorous definition of what it means to compute something "without" computing something else. It would be more accurate to say that their algorithm uses very small space; but even this claim is not fully proved, due to the fact that we don't know (for example) about the distribution of blocks of 1's in the binary expansion of π.
Filipe:
Not really. Although there are methods for computing isolated bits or blocks of bits, they are not at all competitive with "starting from scratch", at least when you want to compute millions or billions of digits.
The pi searcher tells us:
pi = 3.1415926...197297159417005[b]31415926[/b]095214704122509...
In response to anonymous in reference to the 2,699,999,990,000 limit...
Although he may have picked an arbitrary value, I am thinking it has to do with some kind of limitation on the system that the calculation was being done on.
I've written prime number generators, and once I fined tuned the algorithm based on the speed of calculating the prime numbers from 1 to 1,000,000, I decided to let my computer just churn away....
I as not thinking as far ahead and when I reached 4,294,967,295 my program crashed. I had been incrementing a integer variable that was 32 bits (4 bytes) and when it it tried to increment past that value it actually wrote over another bit in memory...apparently an important one, and the program crashed.
Obviously he though a little further ahead in his calculation than I did, at some point you will run out of system memory to continue on.
I think that it is simply wonderful that this record was broken with a home computer. Of course you can break new ground with a pen and paper to.
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