Message 6988 from Yahoo.Groups.Primeform

Return-Path: <jgchilders@...> X-Sender: jgchilders@... X-Apparently-To: Received: (qmail 48010 invoked from network); 24 Feb 2006 18:58:26 -0000 Received: from unknown ( by with QMQP; 24 Feb 2006 18:58:26 -0000 Received: from unknown (HELO ( by with SMTP; 24 Feb 2006 18:58:26 -0000 Comment: DomainKeys? See Received: from [] by with NNFMP; 24 Feb 2006 18:58:22 -0000 Received: from [] by with NNFMP; 24 Feb 2006 18:58:22 -0000 Date: Fri, 24 Feb 2006 18:58:21 -0000 To: Message-ID: <dtnl0d+adf9@...> User-Agent: eGroups-EW/0.82 MIME-Version: 1.0 Content-Type: text/plain; charset="ISO-8859-1" Content-Transfer-Encoding: quoted-printable X-Mailer: Yahoo Groups Message Poster X-Yahoo-Newman-Property: groups-compose X-Originating-IP: X-eGroups-Msg-Info: 1:12:0:0 X-Yahoo-Post-IP: From: "gchil0" <jgchilders@...> Subject: Primality proof of (34*10^15768-43)/9 - need help! X-Yahoo-Group-Post: member; u=122509175; y=426hkG8M3GXDbIKxuQCXqg2Ui2dlAthEYZhw81iF41g5 X-Yahoo-Profile: gchil0
Hello, Updating the database of factors of 10^n +/- 1 located in the files area of the Primefactors group reminded me that the palindrome N=3D(34*10^15768-43)/9 still hasn't been proven prime. Even though it's no longer even close to a record for the largest palindromic prime with prime digits, I think it's worthwhile doing for completeness. Since 10^15768-1 is 27% factored, this is now possible with the new CHG code of John Renze and David Broadhurst. I proceeded as follows: 1. I extracted all of the PRP factors of 10^15768-1 from the database, added the factors of 34 and removed 9 of course, and proved all but one of them prime using VFYPR. 2. I performed the BLS tests using PFGW using these prime factors in a helper file. 3. I created a CHG input file and started the code running. I had to adjust the precision a couple of times to avoid errors, and it appears \p9000 worked. The search for factors congruent to 1 completed overnight on my Opteron. Since F=1 in this case, the search for factors congruent to n is unnecessary, so a certificate was output. I think there is a bug in the code, however, since at this point it began a search for factors congruent to n. It also claimed to have run David's verifier on the certificate, but since I don't have the verifier, it could not have. So, at this point, there is one missing bit. The primality of the 2454-digit PRP Phi(7884,10)/(3951358309*43519681*11668781326071061*50594869824289387600141* 698321409620914728282889*10226827901261393154083521*2768214255974519676483980192126941) remains to be proven. This is where I need help. Primo would make easy, if time consuming, work of this, but since I'm in the US, the Primo license prohibits me from using it. Could someone outside of the US, Canada, and Japan prove the primality of this number? It would also be nice for someone (David?) to independently verify the CHG certificate. It can be downloaded from Thanks, Greg
Message 6989 Message 6990 Message 6991 Message 6992 Message 6993 Message 6994

Message 6995 Message 6998 Message 7003 Message 7006 Message 7024 Message 7033