Message 3390 from Yahoo.Groups.Primeform

Return-Path: <d.broadhurst@...> X-Sender: d.broadhurst@... X-Apparently-To: Received: (qmail 23693 invoked from network); 27 Jun 2003 22:13:38 -0000 Received: from unknown ( by with QMQP; 27 Jun 2003 22:13:38 -0000 Received: from unknown (HELO ( by with SMTP; 27 Jun 2003 22:13:38 -0000 Received: from [] by with NNFMP; 27 Jun 2003 22:13:34 -0000 Date: Fri, 27 Jun 2003 22:13:34 -0000 To: Subject: Record palindromic prime with prime digits Message-ID: <bdifie+5qjs@...> User-Agent: eGroups-EW/0.82 MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Length: 1234 X-Mailer: Yahoo Groups Message Poster From: "David Broadhurst" <d.broadhurst@...> X-Originating-IP: X-Yahoo-Group-Post: member; u=35890005 X-Yahoo-Profile: djbroadhurst
Phil Carmody and I were playing strange base-10 games, in the wake of In comparison with those mind-bending exercises, it was rather simple to improve on Hans Rosenthal's ECPP-intensive record > (35*10^4157-53)/99 4157 c17 02 ECPP, palindrome also noted in Until today, this was: 1) "The largest known prime with only two different prime digits" and also, in the Dubner-Ondrejka base-10 olympic games: 2) the largest known palindromic prime with all of its digits prime. Both of these records were surpassed in a few hours today, thanks to a speedy search-and-proof routine enabled by OpenPFGW, and also thanks to the Cunningham project, for a 40% factorization of 10^4260-1: Primality testing (30*R(15)+4)*R(4260)/R(15)-1 [N-1/N+1, Brillhart-Lehmer-Selfridge] Calling N+1 BLS with factored part 40.35% and helper 0.10% (121.17% proof) (30*R(15)+4)*R(4260)/R(15)-1 is prime! with a helper file that enables the OpenPFGW proof that the 4261-digit palindrome 33333333(333333373333333)_{283}33333333 is prime. David Broadhurst