mersenneforum.org Factorization attempt for a c214 regards Odd Perfect Numbers
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 2005-06-11, 20:34 #1 jchein1   May 2005 22·3·5 Posts Factorization attempt for a c214 regards Odd Perfect Numbers Hi every one, Thanks to everyone who helped the factorization for a c163 I posted a couple weeks ago. Before I finish my OPN (9 distinct factors) project, I need to get a complete factorization for a c214, which is a factor of 7^343 -1. I am pretty sure c214 is the last roadblock for this project. The completed factorization is 7^343 - 1 = 7^(7^3) - 1 = 2 * 3 * 29 * 4733 * 3529 * 1074473 * 13473433 * 6106505825833677713 * 1373 * 8233 * 49393 * 734021 * 83517610741606021 * 8403170201386002840476080703299123251286617419186485806798706989812597310995759101855982323436346453490295844838291326800248443089057721410790484991729444190401836892041621145614063665607931920955659505589620515021 (c214) I have now completed the 1115 th curve with limit B1=11000000; B2=1100000000 at the 30 digit level on a slow machine utilizing Dario Alpern’s ecm software without luck. Please help and thank you in advance. Regards Joseph E.Z. Chein
 2005-06-11, 20:41 #2 VJS     Dec 2004 13·23 Posts What else have you done? P-1 to what bounds how about P+1 etc?
 2005-06-11, 20:53 #3 akruppa     "Nancy" Aug 2002 Alexandria 2,467 Posts I've started ECM with B1=11M. The SNFS difficulty is 248 with a sextic - not easy, but feasible if a couple of people help sieving. So even if ECM does not get lucky again, we can definitely factor this one. Alex PS. : I've done P-1 with B1=10^8 and am currently doing 10^9. Last fiddled with by akruppa on 2005-06-11 at 20:54
 2005-06-11, 22:20 #4 hlaiho     Feb 2005 1D16 Posts 7^343-1 already factored http://www.loria.fr/%7Ezimmerma/records/c120-355 shows that 7^343-1 is already factored completely. 214 7, 343- 8403170201386002840476080703299123251286617419186485806798706989812597310995759101855982323436346453$214 4902958448382913268002484430890577214107904849917294441904018368920416211456140636656079319209556595$ 214 05589620515021 done 1575721793366942921257214180187566081951195327261 Shimoyama 11.08.04 Heikki
 2005-06-12, 04:27 #5 philmoore     "Phil" Sep 2002 Tracktown, U.S.A. 2·13·43 Posts http://www.cerias.purdue.edu/homes/ssw/cun/pmain505 also shows this number as completely factored. (Latest version as of 05 May 2005.) Also check http://www.cerias.purdue.edu/homes/ssw/cun/index.html for the latest update.
 2005-06-12, 15:15 #6 jchein1   May 2005 6010 Posts Dear Heikki, Philmoore, Alex and everyone, Thank you very much for your valuable information. What a pleasure it is to here that c214 has been factored by Shimoyama on 11/08/2004 already. It’s saved me a great deal of time. The completed factorization for c214 is 1575721793366942921257214180187566081951195327261 * p166. Before I close this post, may I ask if you or anyone knows the factorization for c427 = (19^361-1)/ (19^19-1)/ 84216527581 or any factorizations listing of p^n - 1, where p is a prime > 12 with high n’s? Please let me know. I just completed the 346th curve for that c427 without luck. It’s time to call it quits. The c427 is much too big for any existing algorithm. Please don’t try. Many thanks. Regards Joseph E.Z. Chein
 2005-06-12, 15:32 #7 akruppa     "Nancy" Aug 2002 Alexandria 246710 Posts Prof. Richard Brent's tables list factors of a^n+-1 for 12
2005-06-12, 17:41   #8
rogue

"Mark"
Apr 2003
Between here and the

3·2,081 Posts

Quote:
 Originally Posted by jchein1 I just completed the 346th curve for that c427 without luck. It’s time to call it quits. The c427 is much too big for any existing algorithm. Please don’t try. Many thanks.
346 curves with what B1?

2005-06-12, 18:08   #9
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 Originally Posted by jchein1 Dear Heikki, Philmoore, Alex and everyone, Thank you very much for your valuable information. What a pleasure it is to here that c214 has been factored by Shimoyama on 11/08/2004 already. It’s saved me a great deal of time. The completed factorization for c214 is 1575721793366942921257214180187566081951195327261 * p166. Before I close this post, may I ask if you or anyone knows the factorization for c427 = (19^361-1)/ (19^19-1)/ 84216527581 or any factorizations listing of p^n - 1, where p is a prime > 12 with high n’s? Please let me know. I just completed the 346th curve for that c427 without luck. It’s time to call it quits. The c427 is much too big for any existing algorithm. Please don’t try. Many thanks. Regards Joseph E.Z. Chein
Hi,

How big is n?? Please note that if p = 1 mod 4, then p^(kp) - 1, k odd
has an Aurefeullian factorization that might help. Otherwise, Brent's
tables contain all that is publicly known.

2005-06-12, 18:48   #10
wblipp

"William"
May 2003
New Haven

44718 Posts

Quote:
 Originally Posted by akruppa Prof. Richard Brent's tables list factors of a^n+-1 for 12
Richard Brent has a different file that lists factors for an±1 for a and n < 104 and f>109. This would contain any factors of this number known to Richard Brent. Unfortunately, it does not even show the 84216527581 factor that Joseph has already found.

It's also the best source I know for pn-1 with p>12 and "large n" - although p>100 tends to have few factors with exponents above 100 and p>1000 tends to have few factors at all. OddPerfect.org has been contributing to these ranges as we prepare our first factors file.

Last fiddled with by wblipp on 2005-06-12 at 19:03

2005-06-12, 19:04   #11
Keller

May 2004

2810 Posts

Quote:
 [2005-06-12 18:09:58 GMT] Factor: probable factor returned by *CENSORED* (Athlon64_3400+)! Factor=4404877309587482066089969 Method=ECM B1=250000 Sigma=3960452341 [2005-06-12 18:09:58 GMT] Factor: Composite factor returned by *CENSORED*! Factor=581300074856809716701973568238586158736857742091321705834282135094473035267874767143193662215066561450964216295513378827083512261266014915528181747307393455020766994566080615418673082856139346577858493880082791410344804194670771991184755449759234316337033810904130156076844862334402121472790129337859325175391224529499684330384126802642899984651902174095890345457294139663461755277884279214872130395129 Method=ECM B1=250000 Sigma=3960452341
:P

Testing is being continued :)

Last fiddled with by Keller on 2005-06-12 at 19:05

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