Distributed calculation of $\pi$ I want to write a simple distributed software for the calculation of $\pi$. I want to use a formula which is as easy to distribute as possible. I'm thinking of the BBP formula, or something similar (a digit extraction algorithm), since I can distribute specific digits to the clients, and there is no need to perform a centralized summation in the server. Is there a better approach? The requirement is that I want to minimize the job that is needed to be done by the server, and, if possible, I would like not to need arbitrary precision arithmetic. 
 A: I'm sorry if I burst your bubble, but here's the truth.


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*It really would be awesome if there was at least 1 algorithm that allowed you to get any digit of pi while skipping the previous digits, but unfortunately, there are no such algorithms.

*To realistically calculate a noticeable/practical more digits than have already been discovered, you would have to have an INCREDIBLY big beefy powerful computer because the first 12.1 trillion have already been discovered (see here).

*I would suggest you try an already near perfect pi generator that was used to generate the 12.1 trillion digits of pi: y-cruncher

*If you really do want to look in to creating your own pi generator AND you do meet the astounding cpu requirements, then I heavily respect your persperation and also you might want to start your trek here at binary-splitting and here at Chudnovsky, and with that, I hope the the best of luck to you (since it will be hard) .




Also another thing to get you going is I have a theory you might want to think about:

Why not use the Gauss–Legendre algorithm, but instead of caching the bulk of the temporary stuff from the calculations on the RAM, why not temporarily move it over to the hard disk after that specific section has been computated, and move it back to the RAM for the duration of being used again before moving it back to the hard drive again? At first, you may think that this would actually decrease the speed, but its the Gauss algorithm! It converges so incredibly quickly that the time it takes to go the extra mile by using the hard drive for cache could actually probably be well overcompensated by the incredibly quick convergence of the Gauss algorithm, thus resulting in an actual overall increase in performance and a super duper fastly calculated pi in an incredibly small amount of RAM. (Also, you'll need to look at this page for info on speeding up not just your usb, but it also works very well for hard-disks)

Another post to check out: Calculating custom bits of PI in hex or binary without calculating previous bits
