Senior Membership

[Gerson W. Barbosa]

(03-11-2015 11:01 AM)Paul Dale Wrote:  

(03-11-2015 10:25 AM)Thomas Klemm Wrote:  Is there a proof for this? Or is it that we just don't know a similar formula for base 10?

Quite the contrary, the base ten extraction method for pi has been found! I should keep more up to date.

There is also this paper by Xavier Gourdon:

Computation of the n-th decimal digit of π with low memory

Quoting the abstract:

"This paper presents an algorithm that computes directly the n-th decimal digit of π in
sub-quadratic time and very low memory. It improves previous results of Simon Plouffe, later
refined by Fabrice Bellard. The problem of the n-th digit computation in base 2 had already
been successfully treated thanks to the use of appropriate series, but no corresponding formula
for the question in base 10 has been found yet. However, our result is a progress. Another
result in this paper permits to compute directly the n-th decimal digit of π with intermediate
memory size, leading to intermediate time complexity between linear and quadratic."

Gerson.