From: Simon Plouffe Newsgroups: sci.math Subject: Computation of the n'th digit of Pi in base 10. Date: Mon, 20 Apr 1998 07:07:18 GMT Hello, (in answer to many postings about Pi). I see that there are some debates about the possibility of computing Pi in other bases than 2. First of all, we (me and D. Bailey and P. Borwein) have found a way in September 1995 to compute Pi in base 2 (or 16), in our original article, we mention that we did not found similar formulas for base 10. BUT we searched a certain class of formulas only. See http://www.lacim.uqam.ca/plouffe/Simon/MOCpi.ps for the original article or http://www.lacim.uqam.ca/plouffe/Simon/BaileyBorweinPlouffe.pdf in pdf format. Later in November 1996, I have found a way to compute Pi in ANY base with a different algorithm that uses a formula for Pi known since Newton as explained in http://www.lacim.uqam.ca/plouffe/Simon/articlepi.html The algorithm is 'more' general but the price to pay is that it is fairly slow to actually compute it, the time taken is roughly O(n^3) compared to O(n*log(n)) for the algorithm in base 2. Still : the algorithm can compute (let's say) the 10000'th digit of Pi without having to compute the previous digits and with very little memory. Now, what I have found is only a way that proves that it is possible to do it, it is more theoretical than practical, it surely cannot go beyond the 51.5 billion digits that were recently computed by Kanada in Japan. That late algorithm uses those n'th order Borwein-like algorithms and uses a lot of memory and a lot of CPU power but it is the fastest way to do it so far in base 10. Again, it might be that there is actually a better way to compute it very fast (in a probably different way). I am working on this but it might take several weeks, months, centuries, I don't know! :) (see http://www.lacim.uqam.ca/pi/records.html for the latest records of computations including the ones about the n'th binary digits). Simon Plouffe http://www.lacim.uqam.ca/plouffe Plouffe's Inverter at http://www.lacim.uqam.ca/pi/