Path: ...!news.nobody.at!news.swapon.de!fu-berlin.de!uni-berlin.de!not-for-mail From: ram@zedat.fu-berlin.de (Stefan Ram) Newsgroups: comp.misc Subject: Re: Totally OT: Colliding blocks that compute pi Date: 20 Mar 2025 13:24:14 GMT Organization: Stefan Ram Lines: 20 Expires: 1 Mar 2026 11:59:58 GMT Message-ID: References: <87pliek97p.fsf@tilde.institute> Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit X-Trace: news.uni-berlin.de NBp6NfZAsw4H4Yw3ffSiCA68eEEH1b+k7ormOT9z8tJDDF Cancel-Lock: sha1:Q55s7gba2FcW3qcNHdywk/OnThU= sha256:giq1lr7fzhFAeyO3ExHCyip6XzFAvm87+kuL8gj5S1w= X-Copyright: (C) Copyright 2025 Stefan Ram. All rights reserved. Distribution through any means other than regular usenet channels is forbidden. It is forbidden to publish this article in the Web, to change URIs of this article into links, and to transfer the body without this notice, but quotations of parts in other Usenet posts are allowed. X-No-Archive: Yes Archive: no X-No-Archive-Readme: "X-No-Archive" is set, because this prevents some services to mirror the article in the web. But the article may be kept on a Usenet archive server with only NNTP access. X-No-Html: yes Content-Language: en-US Bytes: 2435 yeti wrote or quoted: >I haven't seen this update yet. So far I only bookmarked it in my RSS >feeds for somewhen later. There was a time when mathematicians believed it was impossible to calculate a specific digit of pi without computing all preceding digits. This belief persisted until the discovery of the Bailey–Borwein–Plouffe (BBP) formula in 1995. The BBP formula allows for the extraction of any arbitrary digit of pi in its binary expansion (base 2) without calculating prior digits. This was groundbreaking and contrary to earlier assumptions. In 1996, Simon Plouffe extended this concept to base 10, enabling the calculation of specific decimal digits of pi without computing all preceding digits, though at a computational cost of O(n^3 (log n)^3), later improved to O(n^2) by Fabrice Bellard. Before these developments, no such efficient "digit extraction" algorithms were known, and it was widely assumed that such methods were not possible.